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1e99fb86df98edf9
motif_ball_tracking
ball_tracking_naive
**Rules:** 1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion; 2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1; 3. The black boundaries of the image represent solid walls. When the ball hit...
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1
1
2
The question asks which of the three top holes the ball enters first. In the input the red ball sits just inside the left wall and the green arrow points up and to the left, so the ball strikes the left wall before the top. Where it later meets the top wall depends on that bounce and cannot be read off directly. I will...
In this picture the first segment runs from the ball to the left wall, where the red dot sits, and the dashed horizontal line marks the horizontal component that must reverse. After the bounce the ball keeps its steep upward motion but now travels up and to the right at the same slant. Where that second segment meets t...
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The extended map shows the full path: from the ball to the left wall, then up and to the right, meeting the top wall at the red dot. That crossing lies well inside the leftmost cell, clearly to the left of the wall between hole 1 and hole 2, so the ball passes straight through the opening of hole 1. Since the ball ente...
train
mit
procedural_grid
10,054
S5.replay_unsupported,S8.phash_near_but_distinct
281d48703f70fae4
motif_ball_tracking
ball_tracking_naive
**Rules:** 1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion; 2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1; 3. The black boundaries of the image represent solid walls. When the ball hit...
null
3
1
1
I need which top hole the ball enters first. The input shows the ball in the lower-right of the box with a green arrow pointing up-left, so it moves diagonally toward the top. By eye the slope and start don't reveal which span the diagonal crosses. So I sketch a top-down map with the five holes across the top, the star...
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On the map the straight line from the lower-right start rises up-left and meets the top edge with its red dot sitting just to the left of the divider between holes 3 and 4, i.e. inside hole 3's span. The line never touches a side wall before reaching the top, so there is no reflection to reroute it. The ball therefore ...
train
mit
procedural_grid
8,505
S5.replay_unsupported
41f5c14cc201fd58
motif_ball_tracking
ball_tracking_naive
**Rules:** 1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion; 2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1; 3. The black boundaries of the image represent solid walls. When the ball hit...
null
1
1
2
The question asks which top hole the ball enters first. The red ball sits low on the right side and the green arrow points up and to the right, so the ball heads for the right wall before any hole. Where it bounces and where the reflected path meets the top edge are not readable directly, so I will trace the path segme...
The map I sketch shows the ball's first segment climbing up and right until it meets the right wall, with the red dot fixing the bounce point and the dashed blue line marking its height. So the first contact is a wall, not a hole, and the horizontal speed now reverses while the upward speed stays, sending the ball up a...
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In this picture the reflected segment runs from the right-wall bounce point far up and to the left, and the red dot lands on the top edge well to the left of the first divider, i.e. inside the leftmost opening, hole 1. Since that part of the top is a hole rather than a wall, the ball does not bounce again; it falls in ...
train
mit
procedural_grid
10,036
S5.replay_unsupported,S8.phash_near_but_distinct
abac1aabcb37692a
motif_ball_tracking
ball_tracking_naive
**Rules:** 1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion; 2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1; 3. The black boundaries of the image represent solid walls. When the ball hit...
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1
1
2
I need to know which of the four top holes the ball enters first. The input shows the ball low on the right side of the box, the green arrow pointing down and left, so the ball first heads for the bottom wall. From the start alone I cannot see where the path will later meet the top edge, because bounces will redirect i...
The first sketch shows the ball's segment ending on the bottom wall, the red dot sitting just below the seam between holes 3 and 4, with a dashed vertical above the dot. The dashed line says the vertical velocity now points up while the leftward part is unchanged, so after the bounce the ball climbs toward the upper-le...
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In this picture the reflected line rises from the bottom dot to the upper-left and meets the top edge in a red dot. That dot lies under the cell labelled 1, to the left of the seam between holes 1 and 2, so the ball reaches the top inside the span of the first hole. Therefore the ball enters hole 1 first.
train
mit
procedural_grid
10,043
S5.replay_unsupported,S8.phash_near_but_distinct
d3e3d32e868a3287
motif_ball_tracking
ball_tracking_naive
**Rules:** 1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion; 2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1; 3. The black boundaries of the image represent solid walls. When the ball hit...
null
1
1
1
The question asks which top hole the ball enters first. The input shows a red ball near the middle of the box with a green arrow pointing up and to the left, and three rectangular holes numbered 1, 2, 3 along the top edge. The arrow fixes the direction but not how far the ball travels before meeting the top wall, so I ...
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In this picture the straight path from the ball rises to the left and meets the top edge just to the left of the divider between holes 1 and 2, placing it inside the leftmost hole. The ball moves straight until it either bounces or enters a hole, and this very first intersection with the top is already a hole, so no re...
train
mit
procedural_grid
8,536
S5.replay_unsupported
8568eae8ea7cf982
motif_ball_tracking
ball_tracking_naive
**Rules:** 1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion; 2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1; 3. The black boundaries of the image represent solid walls. When the ball hit...
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3
1
4
I need to find which of the four top openings the ball enters first. The input shows a red ball in the right-middle of the box, with a green arrow pointing down-right at roughly a 45-degree slope, and four openings numbered 1 to 4 along the top wall. The ball's first hit will be the right wall, but the exact impact poi...
On this map the first segment ends at a red dot on the right wall, roughly a third of the way down from the top. The dashed line against the vertical wall tells me the horizontal component of the motion reverses, so the ball now travels down-left at the same slope. Where that segment lands is still not readable from he...
The map now shows the second segment ending at a red dot on the bottom wall, left of the middle. Reflecting off the floor reverses the vertical component, so the ball heads up-left at the same slope. Where it meets the left wall is not yet determined, so I extend the map again with a third segment from the bottom dot u...
The map shows the third segment ending at a red dot on the left wall, about mid-height. Bouncing there sends the ball up-right toward the top wall, and since the openings cut through that wall, this next crossing decides which hole it enters. I draw the fourth segment from the left-wall dot up-right until it reaches th...
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In this final map, the fourth segment crosses the top wall at a red dot sitting just beneath the label 3, inside the third opening from the left; it lies to the right of the opening 2/3 boundary and to the left of the 3/4 boundary, so it is not within openings 1, 2, or 4. The ball therefore enters hole 3 first. Answer:...
train
mit
procedural_grid
17,098
S5.replay_unsupported,S8.phash_near_but_distinct
d8b83abada4e8b45
motif_ball_tracking
ball_tracking_naive
**Rules:** 1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion; 2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1; 3. The black boundaries of the image represent solid walls. When the ball hit...
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1
1
2
I need to find which of the three top holes the ball enters first. The input shows the red ball low in the left part of the box, the arrow pointing up and slightly left, and holes numbered 1, 2, 3 across the top. The arrow is short, so I cannot tell whether the ball reaches the top edge or strikes the nearby left wall ...
The map shows the first stretch of the path: from the red start the line runs up-left and meets the left wall at the red dot, well below the top edge. So the ball bounces off the left wall before reaching the top, and after the reflection it travels up and to the right, since the horizontal push reverses. Where that se...
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This picture shows the whole path: the ball leaves the start, bounces off the left wall, then runs up-right to the top edge, where the red dot sits. That dot lies on the top boundary inside the leftmost opening, under label 1, to the left of the divider between holes 1 and 2. The ball can leave the box only through a h...
train
mit
procedural_grid
10,041
S5.replay_unsupported
1165374ed44472bd
motif_ball_tracking
ball_tracking_naive
**Rules:** 1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion; 2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1; 3. The black boundaries of the image represent solid walls. When the ball hit...
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3
1
3
I need to find which numbered hole at the top the ball enters. The input shows the ball low in the left part of the box, and the green arrow points up and left, so the ball first travels toward the left wall, not directly at any hole. Where the path bends after each bounce is not visible from the input alone, so I will...
This picture shows the first segment ending on the left wall: the red dot marks the impact a little above the ball's start, and the dashed line points right, so after reflecting the ball now moves up and to the right. Because the first segment rose only slowly, this reflected path is shallow, and the input alone does n...
The new picture shows the second segment crossing the box and striking the right wall at a point clearly below the top edge, and the dashed line there points left, so the ball now travels up and to the left. What remains open is whether it reaches the top boundary or the left wall first. The slope is gentle enough that...
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The last picture shows the third segment leaving the right wall and ending on the top boundary at a red dot. Reading the top cells, the dot lies to the right of the boundary between cells 2 and 3, inside the cell labeled 3. A hole is an opening in the top wall, and the ball lands exactly on such an opening, so the ball...
train
mit
procedural_grid
13,649
S5.replay_unsupported
ce6ecbff2f9e2203
motif_ball_tracking
ball_tracking_naive
**Rules:** 1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion; 2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1; 3. The black boundaries of the image represent solid walls. When the ball hit...
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2
1
3
The question asks which top hole the ball first enters. The image shows a box with four holes numbered 1 to 4 along the top, a red ball in the lower right, and a green arrow pointing down and left, so the ball moves toward the bottom wall while drifting left. I cannot yet tell which wall it reaches first or where it la...
The map I sketched shows the first contact is on the bottom wall, left of centre, with the dashed vertical line as its normal. That fixes the bounce: the leftward drift continues and the downward motion flips to upward, so the ball now travels up and left. I still do not know which wall that ray meets next. I will ther...
This picture adds the second contact, on the left wall about mid-height, with a dashed horizontal normal. Reflecting there keeps the upward motion and flips the leftward drift to rightward, so the ball now travels up and right toward the top. The open question is which top hole that ray passes through. I will draw this...
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The last picture shows the up-right ray from the left wall meeting the top edge at a red dot that lies in the second cell from the left, between the 1–2 and 2–3 boundary marks, i.e. under hole 2. Because that point of the top edge is an opening, the ball escapes there on this segment before any further bounce can occur...
train
mit
procedural_grid
13,592
S5.replay_unsupported
0114e260ea95f328
motif_ball_tracking
ball_tracking_naive
**Rules:** 1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion; 2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1; 3. The black boundaries of the image represent solid walls. When the ball hit...
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3
1
1
I need the first hole the ball enters. The ball starts in the left-middle of the box and the arrow points up and right, so the top wall is its first possible contact. I cannot settle by eye which numbered cell the straight path crosses at the top, since the meeting point could fall on either side of a middle divider. S...
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On the map, the straight line from the start point meets the top wall at the red dot, which lies just left of the divider between the third and fourth cells, so the crossing is inside hole 3. Since the ball travels in a straight line from its start and this is its first contact with any wall, it bounces nothing on the ...
train
mit
procedural_grid
8,525
S5.replay_unsupported
27b1f75af6e1688b
motif_ball_tracking
ball_tracking_naive
**Rules:** 1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion; 2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1; 3. The black boundaries of the image represent solid walls. When the ball hit...
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3
1
1
The question asks which numbered hole at the top the ball first enters. The input shows the red ball in the upper box with a green arrow pointing steeply up and slightly right. I cannot read off where that slanted flight meets the top edge without carrying it across the box in my head. So I will sketch a map: the box w...
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On this map the straight path leaves the red dot rising up and to the right and ends at a red dot on the top edge. That dot sits inside the third cell, directly beneath the label 3, so the flight crosses the top boundary through the third opening. This is the ball's first contact with the top, before any wall bounce co...
train
mit
procedural_grid
8,524
S5.replay_unsupported
edfda5e7816ad30e
motif_ball_tracking
ball_tracking_naive
**Rules:** 1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion; 2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1; 3. The black boundaries of the image represent solid walls. When the ball hit...
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2
1
2
I must find which of the three top holes the ball enters first. The image shows a red dot near the middle of the box and a green arrow pointing upper-right at a shallow angle, so the ball drifts right while climbing slowly. Whether it reaches the right wall before the top, and where that bounce lands, is not readable b...
In the map, the path from the red dot runs up and to the right, meeting the right wall well below the top edge at the marked red dot; the first bounce is off the right wall, not a hole. By reflection the horizontal component reverses while the upward climb continues, so the ball now heads up and to the left. Where that...
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The extended map shows the ball leaving the right-wall mark upward and to the left, crossing the top boundary at the red dot that sits inside the middle opening, between its two dividers and directly beneath label 2. This is the first place the path touches the top, so the ball drops through that opening before any lat...
train
mit
procedural_grid
10,038
S5.replay_unsupported
1bc3dd33b400aa7d
motif_ball_tracking
ball_tracking_naive
**Rules:** 1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion; 2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1; 3. The black boundaries of the image represent solid walls. When the ball hit...
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2
1
3
The question asks which top hole the ball enters. The input shows the red ball near the box center with a green arrow pointing down and left, so the ball first moves diagonally toward the bottom wall. The arrow alone does not say where it strikes or what later bounces do, so I track the path segment by segment. I sketc...
The map shows the first segment: from the ball's start it runs down and left and ends at a red dot on the bottom wall, in the left part of the box. So the ball's first bounce is off the bottom, and after it the downward component flips while the leftward one keeps going, meaning the ball now travels up and left. Where ...
This picture shows the second bounce: the path rises from the bottom point up and left to a red dot in the lower part of the left wall, with a horizontal dashed tick at the contact. The leftward component now reverses, so after this bounce the ball travels up and right. The only thing left to know is where that diagona...
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The last picture shows the full path: down and left to the bottom wall, up and left to the left wall, then up and right to the top edge, where a red dot marks the crossing. That dot lies in the top bar between the divider after hole 1 and the divider after hole 2, in the cell labelled 2, just left of the boundary betwe...
train
mit
procedural_grid
13,620
S5.replay_unsupported
bde0547b452a44ab
motif_ball_tracking
ball_tracking_naive
**Rules:** 1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion; 2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1; 3. The black boundaries of the image represent solid walls. When the ball hit...
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3
1
3
The question asks which of the five top holes the ball enters first. I see the red ball mid-box with a green arrow pointing down-left. From that alone I cannot tell whether it strikes the bottom or the left wall first, where it lands, or which top hole the later bounces lead to. So I will sketch the path: extend the ar...
The sketch shows the first stroke ending on the bottom wall, near the left corner, so the first bounce is settled. At a horizontal wall the vertical component reverses while the leftward component stays, so the ball now climbs up and to the left; already being near the left edge, it should hit that wall after only a sh...
This picture adds the second stroke: it climbs from the bottom bounce to a point on the left wall fairly low down. With the first two bounces fixed, at this vertical wall the horizontal component flips to rightward while the upward component stays, so the ball runs a long diagonal up-right whose next wall is the top. W...
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The completed map shows the third stroke meeting the top wall at a red dot just to the right of the 2-3 boundary, inside hole 3. The first two bounces were on the bottom and left walls, so this is the ball's first reach of the top, and it lands at a hole. Therefore the ball enters hole 3 first. Answer: 3.
train
mit
procedural_grid
13,553
S5.replay_unsupported
30400afc47fd81a7
motif_ball_tracking
ball_tracking_naive
**Rules:** 1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion; 2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1; 3. The black boundaries of the image represent solid walls. When the ball hit...
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2
1
1
I need the hole the ball enters first. The input shows the red point low on the left, a green arrow pointing up-right, and a top edge split into three openings numbered 1, 2, 3. The arrow fixes the direction but not the landing point, so I cannot yet tell whether the straight path meets the top boundary over hole 1, 2,...
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In the map I sketch, the straight line from the ball's starting position climbs up-right and ends at the red dot on the top boundary. That dot lies between the divider after hole 1 and the divider after hole 2, well inside the second opening, not in hole 1 or 3. The top boundary is the first wall the path reaches, and ...
train
mit
procedural_grid
8,527
S5.replay_unsupported
579b6294ffdb34ec
motif_ball_tracking
ball_tracking_naive
**Rules:** 1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion; 2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1; 3. The black boundaries of the image represent solid walls. When the ball hit...
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3
1
1
I need to find which of the three top holes the ball enters first. The box shows the red ball near the middle, with a short green arrow pointing up and to the right, and three holes numbered left to right along the top edge. The ball travels in a straight line at constant speed until it meets a wall or a hole, so the f...
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On the map, the straight line from the ball's position runs up and to the right and meets the top wall at a single point, marked by the red dot, lying just to the right of the divider between holes 2 and 3. That point falls inside the span of hole 3. The ball reaches the top boundary there for the first time of its mot...
train
mit
procedural_grid
8,638
S5.replay_unsupported
3f44901babe64722
motif_ball_tracking
ball_tracking_naive
**Rules:** 1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion; 2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1; 3. The black boundaries of the image represent solid walls. When the ball hit...
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1
1
1
I need the hole, among the four top holes numbered 1 to 4 left to right, that the ball enters first. The input shows a red point on the right side of the box and a green arrow pointing upper-left, so the ball's first motion is a straight line toward the upper-left. I cannot tell by eye which gap the line crosses. So I ...
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On the map, the straight segment runs from the ball's starting position on the right side up toward the upper-left, and it meets the top boundary at a red dot. Reading the dot against the row of holes, it sits inside the span of hole 1, left of the dividing line between holes 1 and 2. The segment touches no wall before...
train
mit
procedural_grid
8,526
S5.replay_unsupported
a84c08059f2674cc
motif_ball_tracking
ball_tracking_naive
**Rules:** 1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion; 2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1; 3. The black boundaries of the image represent solid walls. When the ball hit...
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2
1
3
I need to know which top hole the ball falls into. The red ball sits in the left-middle of the box and the green arrow points down-left, so it will reach the bottom edge near the lower-left corner first, but the exact impact and the bounces after it are hidden in the reflections and must be traced. I will sketch a map ...
The map shows the first leg ending in a red dot on the bottom edge just right of the lower-left corner, and the dashed tick shows the ball is a hair from the left wall. The bottom bounce flips only the vertical part, so the ball now travels up-left and strikes the left wall almost at once; that second bounce point and ...
This picture places the second bounce on the left wall, very low, just above the corner, with a blue dashed line pointing right from the dot. That settles the second reflection: the left-wall bounce flips the horizontal part, so the ball now climbs up-right at the same slope, and this long leg carries it to a hole. Whe...
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In this last picture the long up-right leg ends in a red dot on the top edge. The dot lies between the two vertical dividers of the middle cell, directly beneath the label 2, not over cell 1 or cell 3. Since the ball enters a hole the moment it reaches the top within that hole's span, and this is the first time its pat...
train
mit
procedural_grid
13,604
S5.replay_unsupported
b492591b0889b98a
motif_ball_tracking
ball_tracking_naive
**Rules:** 1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion; 2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1; 3. The black boundaries of the image represent solid walls. When the ball hit...
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2
1
2
I need to determine which of the four top holes the ball enters. The input shows the red ball in the left-center of the box, the green arrow pointing up and left, so the ball travels leftward and upward. Its aim is too shallow to reach the top before the left wall, so the first event is a bounce there, and the bounce h...
The map shows the first segment ending at the left wall below its mid-height, with the red dot at that impact and the dashed normal running horizontally. That settles where the ball bounces. What is open is where the reflected path meets the top: after the bounce the horizontal part of the motion points right while the...
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In this picture the reflected line runs from the left-wall bounce up to the top boundary, and the red dot lands on that boundary to the right of the divider between holes 1 and 2 and to the left of the divider between holes 2 and 3, i.e. under the second opening. The ball has not hit anything since the first bounce, so...
train
mit
procedural_grid
10,049
S5.replay_unsupported
fb4d2bedf88a0338
motif_ball_tracking
ball_tracking_naive
**Rules:** 1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion; 2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1; 3. The black boundaries of the image represent solid walls. When the ball hit...
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4
1
1
I need the first hole the ball enters. The input shows a red ball near the middle of the box and a green arrow pointing up-right, so its first straight run heads toward the upper-right. By eye I cannot say whether that run ends on the top wall or the right wall, nor which opening it would cross, since the landing spot ...
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On the map, the segment leaves the ball and rises to the right, meeting the top wall at the red dot. That dot sits between the two grid lines that bound the opening labeled 4, directly under its number, not in 3 or 5. Because the top wall is an opening at that spot, the ball passes straight through on this very first s...
train
mit
procedural_grid
8,507
S5.replay_unsupported
182975dbdea131e1
motif_ball_tracking
ball_tracking_naive
**Rules:** 1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion; 2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1; 3. The black boundaries of the image represent solid walls. When the ball hit...
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1
1
I need to know which top hole the ball reaches first. The input shows a red ball in the lower-middle of the box with a green arrow pointing up and to the right, and three holes numbered 1, 2, 3 across the top. The arrow fixes the initial direction, but the point where the ball meets the top wall is not marked, and I ca...
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On the map I sketch, the line leaves the ball going up and to the right and crosses the top boundary at the marked dot. That dot sits well to the right of the divider between holes 2 and 3, inside the span of hole 3, and the line reaches it without touching any side wall. So the path is one unbroken straight segment fr...
train
mit
procedural_grid
8,573
S5.replay_unsupported
62112b51013e1b60
motif_ball_tracking
ball_tracking_naive
**Rules:** 1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion; 2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1; 3. The black boundaries of the image represent solid walls. When the ball hit...
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1
2
I need to know which of the four numbered holes along the top the ball drops into first. The input shows the ball low in the box, its arrow aimed up and to the right, so its first straight run heads toward the top edge and the right wall. Which boundary it reaches first, and where along the top edge it arrives relative...
On the map I sketched, the extended path climbs to the upper right and terminates exactly at the corner where hole 4 meets the right wall; a short dashed line runs along the top inside hole 4, showing the path ends at the very last stretch of that hole. So the ball is aimed at the boundary between hole 4 and the right ...
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In this refined view the crossing marker sits on the top boundary inside hole 4: clearly to the right of the divider between holes 3 and 4 and clearly to the left of the right wall. The ball's first straight run therefore passes through the opening of hole 4 before it ever touches a solid wall, so no reflection happens...
train
mit
procedural_grid
10,116
S5.replay_unsupported
dffd82f3013298be
motif_ball_tracking
ball_tracking_naive
**Rules:** 1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion; 2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1; 3. The black boundaries of the image represent solid walls. When the ball hit...
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1
2
I need to find which top hole the ball falls into. The input shows the red ball low and to the left of center, with the green arrow pointing up and to the left at roughly a diagonal. That alone does not settle the path: I cannot be sure by eye whether the ball reaches the left wall before the top edge, at what height i...
This map shows the first segment: the ball travels up-left and meets the left wall well below the top edge, so its first contact is the side wall, not a hole. With the ball at the left wall and the horizontal dashed normal marked, the reflection is straightforward: the upward component is unchanged and the leftward hor...
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The extended map shows the whole route: up-left to the left wall, then up-right, where the segment meets the top edge at the divider between holes 2 and 3, i.e. at the left edge of hole 3, marked by the red dot. Before this crossing the ball has only touched the left wall and entered no hole, so this is its first entry...
train
mit
procedural_grid
10,187
S5.replay_unsupported
8c736de8a10ce0ff
motif_ball_tracking
ball_tracking_naive
**Rules:** 1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion; 2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1; 3. The black boundaries of the image represent solid walls. When the ball hit...
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1
2
I need to know which top hole the ball falls into. The input shows the ball near the bottom-right corner, arrow pointing up and to the right, so it strikes the right wall first, not the top edge with its four numbered spans. From the start alone I cannot read off where the reflected segment lands, since the bounce flip...
The map puts the strike point on the right wall, well below the top edge. The incoming path arrives from the lower left and the dashed guide marks the horizontal direction at that point; after the bounce the horizontal part reverses, so the ball leaves toward the upper left. That settles the first bounce, but not which...
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In this last picture, the second segment runs from the right-wall dot up and to the left and meets the top edge at the red dot, which sits just to the right of the line separating the first and second spans, i.e., within the span labeled 2, not in span 1 or 3. Since the ball travels straight along this segment and the ...
train
mit
procedural_grid
10,072
S5.replay_unsupported,S8.phash_near_but_distinct
4aae317d78c8eb87
motif_ball_tracking
ball_tracking_naive
**Rules:** 1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion; 2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1; 3. The black boundaries of the image represent solid walls. When the ball hit...
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1
3
The question asks which of the five top holes the ball enters. The input shows the red ball low in the box, left of center, with the green arrow pointing down-right, so the first hit is the bottom wall, not a hole. From the start alone this is not settled: the bottom impact point and the reflected direction must be con...
This map shows the first segment running down-right from the old ball position to a red dot on the bottom wall, left of the box's middle, with a dashed vertical normal at the impact. That settles the bounce point. Still open is where the ball goes next: the vertical component of the velocity flips while the horizontal ...
This view shows the second segment rising from the bottom bounce to a red dot high on the right wall, with a dashed horizontal normal there. So the ball strikes the right wall, not the top, and the second bounce point is settled. What remains is the direction after this bounce: the horizontal component flips, so the ba...
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The last extension leaves the right-wall bounce and runs up-left, ending at a red dot on the top boundary. Reading the numbered row, that dot lies in the rightmost gap: to the right of the line separating holes 4 and 5, and to the left of the right wall. The ball has not crossed the top edge anywhere before this, so th...
train
mit
procedural_grid
13,602
S5.replay_unsupported
20466289a131fde6
motif_ball_tracking
ball_tracking_naive
**Rules:** 1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion; 2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1; 3. The black boundaries of the image represent solid walls. When the ball hit...
null
3
1
1
The question asks which top hole the ball enters first. The input shows the red ball low in the left part of the box, with the green arrow pointing up and to the right. Where that slanted path meets the top edge cannot be trusted by eye, and the ball might bounce off a side wall first, so I will draw the path. I sketch...
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On my sketch, the straight line from the ball's start climbs up and to the right and meets the top boundary at the red dot, which sits just left of the divider between holes 3 and 4, so it falls inside the opening labelled 3. The line crosses no side wall on the way, so there is no earlier reflection; the ball's first ...
train
mit
procedural_grid
8,510
S5.replay_unsupported
61c30a9d2f54bc11
motif_ball_tracking
ball_tracking_naive
**Rules:** 1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion; 2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1; 3. The black boundaries of the image represent solid walls. When the ball hit...
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4
1
3
I must find which of the five top openings the ball falls into. The start frame shows the ball in the left-middle of the box with an arrow pointing down and to the right, so the ball heads toward the lower-right region. The first wall it can meet is either the bottom or the right side, and after any bounce the directio...
The map shows the first segment leaving the ball and striking the bottom wall right of its middle; the red dot and vertical dashed tick mark that impact. So the bounce keeps the rightward component and flips the downward one: the ball now travels up and to the right. From that point the next wall must be the top or the...
In this map the path forms a V: the first segment to the bottom wall, then a steep up-right segment ending at the right wall, with the red dot and horizontal dashed tick at the impact. At the right wall the horizontal component reverses, so the ball now travels up and to the left. The open question is exactly where thi...
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The finished map shows the third segment leaving the right wall and rising to the top edge, where the red dot sits inside the fourth opening from the left, just to the left of the divider between the 4 and 5 cells. The ball reaches the top exactly at an opening, so it drops in there rather than reflecting. The first ho...
train
mit
procedural_grid
13,678
S5.replay_unsupported
862b26485adcd0e3
motif_ball_tracking
ball_tracking_naive
**Rules:** 1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion; 2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1; 3. The black boundaries of the image represent solid walls. When the ball hit...
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2
1
1
I need to determine which top hole the ball enters first. The input shows the red ball in the upper-middle of the box with the green arrow pointing up and to the left, so the ball initially moves toward the top wall. The arrow is too short to see where its line of travel meets the top boundary relative to the hole edge...
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On this map, the red dot marks where the ball's straight path meets the top wall: it lies just to the right of the divider between holes 1 and 2, so it falls within the span of hole 2. The line from the ball up to this dot touches no side wall, so the ball has not reflected yet when it arrives. Since the crossing point...
train
mit
procedural_grid
8,569
S5.replay_unsupported
fc5cf4dbc6ced801
motif_ball_tracking
ball_tracking_naive
**Rules:** 1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion; 2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1; 3. The black boundaries of the image represent solid walls. When the ball hit...
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1
1
3
I need to find which top hole the ball enters first. The input shows a red ball in the lower right of a square box, with a green arrow pointing down and to the right, so the ball initially travels toward the right wall. From the picture alone I cannot tell where it bounces or which of the three top cells it eventually ...
The map I sketch shows the first segment ending in a red dot on the right wall, well above the bottom corner, so the ball strikes the right side first. That fixes the first bounce. What remains open is the next leg: after an ideal reflection the horizontal part of the velocity reverses while the downward part continues...
Now the map shows two bounces: the right wall, then a point on the bottom wall left of the right corner, beneath the span of the rightmost top cell. After this bottom bounce the vertical part of the velocity reverses, so the ball heads up and to the left at the same slope it came in with. It has a long way to go, and i...
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The last map shows the third segment rising from the bottom bounce up and to the left, crossing the top boundary at a red dot that lies inside the leftmost cell, clearly to the left of the divider between cells 1 and 2. Since the path reaches the top at that point before meeting any other wall, the first hole the ball ...
train
mit
procedural_grid
13,661
S5.replay_unsupported
2923743a24d4cef4
motif_ball_tracking
ball_tracking_naive
**Rules:** 1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion; 2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1; 3. The black boundaries of the image represent solid walls. When the ball hit...
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1
1
The question asks which top hole the ball enters first. In the input the red ball sits in the lower right and the green arrow points up and left at about forty‑five degrees; the three holes line the top edge. I cannot trust my eye for where the straight line from the ball meets that top edge, so I will sketch the box w...
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In the map I sketch, the line from the ball's starting dot in the lower right runs straight up and left, and it meets the top edge at the red dot that lies inside the leftmost hole, hole 1, near its right side. The line never touches a side wall before that point, so no reflection occurs and this single straight segmen...
train
mit
procedural_grid
8,508
S5.replay_unsupported
2bf189b7414f2882
motif_ball_tracking
ball_tracking_naive
**Rules:** 1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion; 2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1; 3. The black boundaries of the image represent solid walls. When the ball hit...
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2
1
1
The question asks which top opening the ball enters first. The input shows the red ball in the left-middle with a green arrow aimed up and slightly right, so it moves up-right toward the top's four openings, numbered 1 to 4. I cannot tell by eye which opening the slanted line crosses, as the steep arrow over a long run...
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On my map the line leaves the ball's spot and climbs up-right, meeting the top edge at the red dot. That dot sits inside the second opening from the left, close to its right edge but still on the 2 side of the divider, not in opening 3. Because this is the ball's first contact with the top and it lands on an open span ...
train
mit
procedural_grid
8,534
S5.replay_unsupported
6637e1f3c71111a2
motif_ball_tracking
ball_tracking_naive
**Rules:** 1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion; 2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1; 3. The black boundaries of the image represent solid walls. When the ball hit...
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1
3
I need to know which of the three top holes the ball falls into. The image shows the red ball near the middle of the box with the green arrow pointing down and slightly left, so the ball first moves toward the bottom wall, down-left. The starting picture alone does not settle it: after the bounce the line of flight cha...
In this map the first piece of the path runs down-left from the ball and meets the bottom wall at a point well left of the ball's starting column, marked by the red dot. That settles the first bounce. At a horizontal wall the downward part of the motion reverses while the leftward part continues, so the next piece of t...
The extended map shows the second piece climbing from the bottom impact up to the top boundary at the very left corner of the box. The red dot there, with the short dashed line running rightward along the top edge, places the crossing at the left end of hole 1's span, far left of the divider between holes 1 and 2. So t...
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In the final map the path is: from the ball down-left to the bottom wall, then up-left, ending where the top boundary is open. The red dot sits on the top edge at the left end of hole 1's span, clearly left of the first divider between holes 1 and 2, so the ball's straight flight carries it through that opening before ...
train
mit
procedural_grid
13,676
S5.replay_unsupported
7df2d723cf52ea4a
motif_ball_tracking
ball_tracking_naive
**Rules:** 1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion; 2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1; 3. The black boundaries of the image represent solid walls. When the ball hit...
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3
1
3
The question asks which of the four top holes the ball enters first. The input shows the red ball in the right-middle of the box, with the green arrow pointing down and to the left, so the ball's first motion is toward the lower-left. The box is otherwise empty, and the four numbered openings sit only along the top edg...
In this picture the first segment runs from the starting point down-left and meets the bottom wall at a point left of center; the short dashed vertical line marks the normal there. That settles the first hit: the bottom wall, not the left one. After an ideal reflection the vertical component reverses while the horizont...
This picture now shows the full V: after the bottom hit, the second segment rises up-left and meets the left wall at about mid-height, with a dashed horizontal normal at that red dot. The second reflection is settled. Reflecting off the left wall reverses the horizontal component, so the ball now travels up-right, aime...
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In this final picture the third segment leaves the left-wall point up-right and reaches the top edge at a red dot sitting just to the right of the line between holes 2 and 3, inside the third opening. The top edge is solid except at the holes, so when the path crosses it within an opening the ball falls in there. The c...
train
mit
procedural_grid
13,692
S5.replay_unsupported
41960af55af42f8d
motif_ball_tracking
ball_tracking_naive
**Rules:** 1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion; 2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1; 3. The black boundaries of the image represent solid walls. When the ball hit...
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3
1
1
The question asks which numbered hole at the top the ball enters first. The input shows a red ball left of center with a green arrow pointing up and to the right, and four holes numbered 1 to 4 along the top. The arrow is short, so where its extension meets the top wall is not visible and must be projected. I will sket...
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In the map I sketched, the extended line from the ball meets the top wall at the red dot. That dot sits on the part of the wall spanning the third hole: it is right of the divider between holes 2 and 3 and left of the divider between holes 3 and 4, directly under the label 3. Since the ball moves in a straight line up ...
train
mit
procedural_grid
8,545
S5.replay_unsupported
f411bf4782fc5099
motif_ball_tracking
ball_tracking_naive
**Rules:** 1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion; 2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1; 3. The black boundaries of the image represent solid walls. When the ball hit...
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2
1
1
I need to find which top hole the ball enters first. The input shows a red ball low on the left and a green arrow pointing up and to the right, so the ball's first motion is a straight diagonal. The top edge has three numbered openings, and the ball enters whichever one its path crosses. By eye I cannot be sure where t...
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In this picture the straight line leaves the ball in the lower left and climbs up and to the right until it meets the top boundary. The marked crossing point sits between the divider that ends hole 1 and the divider that ends hole 2, so it lies squarely under hole 2. This is the very first time the path reaches the top...
train
mit
procedural_grid
8,543
S5.replay_unsupported
5fc7e02293d09fa5
motif_ball_tracking
ball_tracking_naive
**Rules:** 1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion; 2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1; 3. The black boundaries of the image represent solid walls. When the ball hit...
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2
1
4
I must find which of the three top holes the ball enters. The input shows the ball near the middle of the box with the green arrow pointing down and to the left at a moderate slope, and three holes along the top wall. Since the ball starts well below the top and moves downward, its first hit cannot be a hole; the first...
The map now shows the first segment: the ball's line runs down-left and the red dot sits on the left wall, roughly two-thirds of the way down; the blue dashed line lies horizontal, the normal to that wall. So the left wall reverses only the horizontal component: the ball leaves heading right, still downward at the same...
This picture adds the second bounce: the red dot is on the bottom wall, just left of its middle, and the blue dashed normal stands vertical. The bottom wall flips the vertical component, so the ball now travels up and to the right, keeping the same shallow slope. Starting from a low point in the left half, that up-righ...
Now the map shows the third segment ending at a red dot on the right wall, about mid-height, with the blue dashed normal horizontal. Reflecting there reverses the horizontal component, so the ball heads up and to the left. This is the first segment that can reach the top wall, where the holes are, so I must place its e...
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The last picture shows the final ray crossing the top edge at a red dot. Reading the top row, the dot lies just right of the divider between holes 1 and 2, and well left of the divider between 2 and 3, i.e., squarely in the middle opening. The path has been left wall, bottom wall, right wall, then the top, and at that ...
train
mit
procedural_grid
17,211
S5.replay_unsupported
2734fdfe24d9d947
motif_ball_tracking
ball_tracking_naive
**Rules:** 1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion; 2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1; 3. The black boundaries of the image represent solid walls. When the ball hit...
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4
1
2
I must find which of the four top holes the ball enters. The input shows a red ball at the left of the box, a green arrow pointing down-right, and four numbered slots across the top. The arrow gives only the initial direction; the ball will bounce before reaching a hole, and the bounce points are not yet visible. So I ...
The map shows the first segment leaving the ball down-right and ending at the bottom wall, at a point left of the box's middle, marked by the red dot with its dashed vertical. That settles the first bounce: it is on the floor, not a side wall. Reflection there reverses only the vertical component, so the ball now trave...
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In the completed map, the second segment rises from the bottom bounce up to the right and meets the top edge at a red dot sitting in the rightmost slot, the fourth one. The path crosses the top boundary inside that last slot, so the ball's first hole is number 4. Since the segment ends exactly at the top edge within th...
train
mit
procedural_grid
10,028
S5.replay_unsupported
68d898fff7d8b01b
motif_ball_tracking
ball_tracking_naive
**Rules:** 1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion; 2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1; 3. The black boundaries of the image represent solid walls. When the ball hit...
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3
1
3
I need to find which of the three top holes the ball enters. The image shows a square box with holes 1, 2, 3 across the top edge; the red ball sits low in the right part of the box and the green arrow points down and to the right. From that alone I cannot tell where the ball finally reaches the top, because it must bou...
The map shows the first segment ending at a dot on the bottom wall, clearly right of the box's middle; the vertical dashed line there fixes how steep the incoming path is. By reflection the perpendicular component flips while the parallel one stays, so the ball now travels up and to the right at the same steepness. Whe...
Now the path runs from the start down to the bottom wall, then up-right to a dot on the right wall in the middle of the side; the horizontal dashed line there shows the incoming direction. Reflection off this vertical wall flips the horizontal component, so the ball now heads up and to the left at the same slope. The o...
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The final picture shows the third segment ending in a red dot on the top boundary. That dot lies to the right of the second divider line and to the left of the right corner, i.e., inside the span labelled 3, and on the way the path has crossed only the bottom wall and the right wall. Since the ball enters a hole the mo...
train
mit
procedural_grid
13,682
S5.replay_unsupported
cc2e56529b11586f
motif_ball_tracking
ball_tracking_naive
**Rules:** 1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion; 2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1; 3. The black boundaries of the image represent solid walls. When the ball hit...
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2
1
1
I need to find which top hole the ball enters first. The image shows a red dot in the lower-left and a green arrow pointing up and to the right, fairly steeply. The direction alone does not tell me where that line reaches the top edge, because I would have to carry that slope across the whole height of the box in my he...
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In the sketch, the straight line from the ball climbs up and to the right and meets the top boundary with the red dot sitting inside the middle cell, the one labeled 2. Because the top edge is open there, the ball does not bounce at all on this first move; it simply travels along this line and falls through that openin...
train
mit
procedural_grid
8,509
S5.replay_unsupported,S14.sampled_qa
684fabd92f4899fe
motif_ball_tracking
ball_tracking_naive
**Rules:** 1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion; 2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1; 3. The black boundaries of the image represent solid walls. When the ball hit...
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2
1
3
The question asks which of the three top holes the ball enters first. The input shows the red ball in the left-middle of the box with a green arrow pointing down-left, so the ball heads for the bottom wall, not straight at any hole. The bounces are not visible yet and the changing direction is hard to follow by eye, so...
The map shows the first piece ending at a red dot on the bottom wall, close to the lower-left corner, with the vertical dashed normal. So the first bounce is off the bottom wall, and since the horizontal velocity is unchanged, the ball now travels up-left. The left wall is only a short distance away, so the next bounce...
This picture adds the second piece: the path now runs from the bottom dot up-left to a red dot on the left wall, slightly above the corner, with a horizontal dashed normal. That fixes the second bounce. After it the horizontal velocity reverses, so the ball heads up-right, and the top edge is far away. To see which hol...
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The last map shows the third piece leaving the left-wall dot, rising to the right, and meeting the top edge at a red dot that sits just right of the boundary between holes 1 and 2, inside the middle opening. That is the ball's first crossing of the top, so it drops into the middle hole. The ball enters hole 2.
train
mit
procedural_grid
13,541
S5.replay_unsupported
f448307faa8ee6d4
motif_ball_tracking
ball_tracking_naive
**Rules:** 1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion; 2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1; 3. The black boundaries of the image represent solid walls. When the ball hit...
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4
1
1
I need to estimate which of the five numbered holes the ball enters. The input shows the red ball in the right part of the box, and the green arrow points from it toward the upper left, so the ball first heads for the top boundary while drifting left as it rises. Where the straight line from the ball in the arrow's dir...
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On the map, the black line runs from the ball's position up and to the left and meets the top boundary at the red dot, which sits inside the fourth hole from the left, between its two dividing lines. The path reaches this opening on the very first flight, before touching any side wall, so no reflection alters it. The b...
train
mit
procedural_grid
8,559
S5.replay_unsupported
c7223e8465006a7f
motif_ball_tracking
ball_tracking_naive
**Rules:** 1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion; 2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1; 3. The black boundaries of the image represent solid walls. When the ball hit...
null
2
1
2
I need to know which of the four top holes the ball enters. The input shows the red ball in the lower-center with the green arrow pointing up and to the left, so the ball first heads for the left wall. Where it strikes, and where it then reaches the top, are not readable from the input; the path must be extended by dra...
The map shows the first segment: a line from the ball's start to a red dot on the left wall, with a dashed blue line at that height; the first bounce is settled. At the vertical wall the horizontal part of the motion reverses and the vertical part stays the same, so the ball now goes up and to the right, but which hole...
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This picture shows the path so far: the first segment from the start to the left wall, then the reflected segment climbing to a red dot on the top edge. Reading that dot against the numbered holes, it lies to the right of the boundary between holes 1 and 2 and to the left of the boundary between 2 and 3, inside the sec...
train
mit
procedural_grid
10,061
S5.replay_unsupported
9e857e97fe93ca34
motif_ball_tracking
ball_tracking_naive
**Rules:** 1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion; 2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1; 3. The black boundaries of the image represent solid walls. When the ball hit...
null
5
1
1
I need to find which of the five top holes the ball falls into. The input shows the ball low in the box, toward the right side, with a green arrow pointing up and to the right. The arrow gives only a short direction hint, and the top strip's cell boundaries are close together, so I cannot tell by eye where the ball's l...
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On my sketch, the line leaves the ball in the lower right and climbs up and to the right, meeting the top boundary at a red dot placed at the far right end of cell 5, right by the corner where the right wall begins. The path crosses the open top edge within cell 5's span before touching any side wall, so no reflection ...
train
mit
procedural_grid
8,545
S5.replay_unsupported
c880ebb5de3ab42a
motif_ball_tracking
ball_tracking_naive
**Rules:** 1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion; 2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1; 3. The black boundaries of the image represent solid walls. When the ball hit...
null
1
1
2
I must decide which of the three top holes the ball enters. The input shows the ball in the lower-left of the box, its arrow pointing upper-left, so the ball heads for the left wall, which lies closer than the top line. Where that impact falls and what direction follows are not visible in the input, so I will sketch a ...
On the map, the first leg ends at the left wall, the red dot sitting well below the top line, roughly midway between the ball's starting height and the top. At this vertical wall the horizontal component reverses, so the ball now travels up and to the right at the same slant. What remains open is where this second leg ...
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In this picture the second leg leaves the left wall and climbs to the top boundary, where the red dot marks the exit. The dot sits between the left edge of the box and the divider between holes 1 and 2, i.e., within the span of hole 1. Since the ball's first reach of the top line is through this opening, it enters hole...
train
mit
procedural_grid
10,029
S5.replay_unsupported
6bed23f87820dd3c
motif_ball_tracking
ball_tracking_naive
**Rules:** 1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion; 2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1; 3. The black boundaries of the image represent solid walls. When the ball hit...
null
3
1
3
The question asks which top hole the ball enters first. The red ball sits in the upper middle of the box, and the green arrow points down and to the right, so the first leg heads toward the lower-right; every hole lies along the top edge, so the ball must bounce before any hole is reachable. I cannot read the impact po...
The map I sketch shows the first leg running from the ball down-right and meeting the bottom wall at a point well right of center, just short of the right side; the red dot marks that bounce, with the blue dashed line standing vertically on the bottom edge there. That settles the first impact: the vertical motion flips...
This picture adds the second leg: from the red dot on the bottom edge the line climbs up-right and meets the right wall below its middle, where a new red dot sits with a short horizontal blue dashed line against the wall. That fixes the second bounce: now the horizontal motion flips while the upward motion continues, s...
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The last picture completes the path. The third leg leaves the right-wall red dot up-left and strikes the top edge at a red dot lying between the divider after the second hole and the divider before the fourth; counting the holes left to right, the dot lands inside the third rectangle, just left of the 3–4 boundary. Sin...
train
mit
procedural_grid
13,740
S5.replay_unsupported
d1f3258a93db2ef5
motif_ball_tracking
ball_tracking_naive
**Rules:** 1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion; 2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1; 3. The black boundaries of the image represent solid walls. When the ball hit...
null
1
1
3
I need which of the three top holes the ball enters first. The input shows the ball in the lower-right region, a green arrow aimed up-right, and a top wall with three holes labeled 1, 2, 3 from left to right. The arrow alone doesn't settle it: the ball's run strikes a wall before any hole, and each bounce redirects it,...
The first map shows the ball's line ending on the right wall, far below the top; the red dot sits at that impact, and the blue dashed line marks the horizontal component that now flips. So the first bounce is off the right wall, and the ball leaves it traveling up-left at the same shallow angle. Whether that reflected ...
This map shows the reflected run from the right wall ending on the left wall, still below the top; the red dot marks the second impact, with the blue dashed line showing the horizontal component that reverses. So the ball has bounced twice, off the right wall then the left wall, and has not yet reached a hole. It now l...
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The final map shows the third run from the left-wall impact rising to the top boundary, where the red dot lands inside the leftmost of the three labeled openings, the cell marked 1 rather than the middle or right one. The ball touches the top wall for the first time exactly at that point, so it passes through that open...
train
mit
procedural_grid
13,666
S5.replay_unsupported
3a502ec7d34f2b8a
motif_ball_tracking
ball_tracking_naive
**Rules:** 1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion; 2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1; 3. The black boundaries of the image represent solid walls. When the ball hit...
null
1
1
3
I need to estimate which of the four top holes the ball falls into. The input shows the red dot in the lower-right region of the box, the green arrow pointing up and to the right at a shallow angle, and the four numbered openings along the top edge. By eye this does not settle it: the ball must bounce off a side wall, ...
The map I sketch shows the first run ending on the right wall: the red dot sits a little above the middle of that wall, and the blue dashed line there is the horizontal part of the motion that reverses. So the ball leaves the right wall still moving upward but now toward the left. Where that up-and-left run ends is not...
This picture shows the second run landing on the left wall close to the top: the red dot sits just below the header row, and the dashed line shows the horizontal component flipping once more. So the ball now travels up and to the right, and since it is already near the top, its next contact must be the top boundary. Bu...
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In this final picture the third segment ends on the top boundary, and the red dot sits squarely inside the span of the leftmost numbered cell, the one marked 1, well clear of the divider between cells 1 and 2. The top line is solid wall except at the openings, so the ball crosses the top exactly at that point and drops...
train
mit
procedural_grid
13,699
S5.replay_unsupported
83bbdb2f20472ad5
motif_ball_tracking
ball_tracking_naive
**Rules:** 1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion; 2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1; 3. The black boundaries of the image represent solid walls. When the ball hit...
null
2
1
3
I need to find which of the three top holes the ball enters. The input shows the ball in the lower-right region with the green arrow pointing down and right, so its first leg runs toward the bottom-right corner of the box. From the input alone I cannot tell which wall it strikes first, bottom or right, because the dire...
On this map, the segment from the ball runs down-right and its red endpoint lands at the corner where the bottom edge meets the right edge, with the blue dashed line highlighting the right wall. The endpoint sits on the bottom line, and the dashed stretch along the right wall shows the ball would still have to travel a...
Now the map shows the incoming segment ending at the corner with the blue dashed line along the bottom edge, confirming the first reflection there: the vertical component reverses, so the ball leaves moving up-right. It is only a hair from the right wall, so it reflects there too and then travels up-left. Where that up...
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This final map shows the complete path: from the ball down to the bottom-right corner, then the reflected line running up-left to the top edge, where the red dot marks the exit. The dot lies on the top line between the two vertical dividers, to the right of the divider ending hole 1 and to the left of the divider begin...
train
mit
procedural_grid
13,748
S5.replay_unsupported
7d6371eba8d6ae8e
motif_ball_tracking
ball_tracking_naive
**Rules:** 1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion; 2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1; 3. The black boundaries of the image represent solid walls. When the ball hit...
null
3
1
3
I need to find which of the three top holes the ball enters first. The input shows the ball sitting low on the left side of the box, with the green arrow pointing shallowly up and to the left. Since the arrow points leftward, the ball must strike the left wall long before it can reach the top, but the input alone does ...
On the map the first line runs from the ball to the left wall at roughly mid-height, comfortably below the top edge, so the first bounce is on the left wall, not in a hole. At a vertical wall the vertical motion is kept and the horizontal motion flips, so the ball now travels up and to the right with the same shallow s...
This picture shows the reflected ray running up and to the right from the left wall point and meeting the right wall just under the top edge, at the far right end of the hole row; the dashed tick there marks the second bounce. So the ball has bounced off the left, then the right wall, still below the top boundary. At t...
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In the last picture the short final line leaves the right wall contact and crosses the top boundary at the red dot. That dot lies inside the right-hand column of the header row, within the span of hole 3: left of its right end and right of the divider between holes 2 and 3. The ball reaches the top for the first time a...
train
mit
procedural_grid
13,708
S5.replay_unsupported
1590487c625e21f8
motif_ball_tracking
ball_tracking_naive
**Rules:** 1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion; 2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1; 3. The black boundaries of the image represent solid walls. When the ball hit...
null
1
1
1
The question asks which of the five top holes the ball enters first. In the input, the red point sits in the lower-middle of the box and the green arrow points up and to the left at roughly 45 degrees. I cannot settle from the eye alone where this line first meets a boundary, because the top wall and the left wall are ...
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In this picture the straight line from the ball rises up and to the left and meets the top edge at the marked red dot, which lies to the left of the divider between holes 1 and 2, inside hole 1's span. This is the first boundary the ball reaches, and at that point the top is an opening rather than a solid wall, so the ...
train
mit
procedural_grid
8,560
S5.replay_unsupported
ed113100b73eb002
motif_ball_tracking
ball_tracking_naive
**Rules:** 1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion; 2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1; 3. The black boundaries of the image represent solid walls. When the ball hit...
null
2
1
1
I need which top hole the ball enters first. The input shows the red ball left of center, the green arrow pointing up-right at 45 degrees, so its first wall hit is the top edge. That edge has three open gaps numbered 1 to 3, so the outcome depends on where the 45-degree line crosses it relative to the two dividers. I'l...
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On the map, the straight line leaves the ball's start heading up-right and meets the top edge at the red dot. The dot lies inside the middle span: past the divider closing hole 1 and before the divider closing hole 2, i.e., within the region labeled 2. Since this is the first wall the ball reaches and the edge there is...
train
mit
procedural_grid
8,512
S5.replay_unsupported
9ec1884268f44ab2
motif_ball_tracking
ball_tracking_naive
**Rules:** 1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion; 2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1; 3. The black boundaries of the image represent solid walls. When the ball hit...
null
3
1
3
I need to find which top hole the ball enters first. The input shows a red ball in the lower-middle of a box, a green arrow pointing down-left, and three numbered holes along the top edge. Since the ball moves down-left, it will strike the bottom wall long before it can reach the top, so the exit is not readable from t...
This picture gives the first segment: from the ball down-left to a point on the bottom wall, far left of the start, marked by the red dot and the blue dashed perpendicular. So the first bounce is at the bottom; the leftward motion continues while the vertical component now points up. What is open is the next wall: trav...
The second segment runs from the bottom bounce up-left to the left wall, low down, where the red dot and the horizontal blue dashed line sit. That settles the second bounce: at the left wall the horizontal component reverses, so the ball now moves up and right, keeping its upward motion. The open question is where this...
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The last picture shows the third segment: a long diagonal from the left wall rising up-right until it meets the top edge, with the red dot exactly at that crossing. The dot lies on the top edge within the span of the third header cell, to the right of the divider between holes 2 and 3 and left of the right wall. So the...
train
mit
procedural_grid
13,624
S5.replay_unsupported
44213b072d106a0e
motif_ball_tracking
ball_tracking_naive
**Rules:** 1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion; 2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1; 3. The black boundaries of the image represent solid walls. When the ball hit...
null
2
1
3
I need to know which of the three top holes the ball falls into. The input shows the ball low in the right side with a green arrow pointing down-left, so it first heads for the bottom wall, while the holes sit in a row along the top. The later bounces are not visible in one glance, so I will sketch a map of the box wit...
On my map, the first leg runs from the start down-left and meets the bottom wall at a point right of center, with a dashed vertical normal at the red dot. A reflection in a horizontal wall keeps the leftward drift and flips the downward motion upward, so the next leg leaves the bottom at the same shallow angle, climbin...
The map now shows two bounces: the bottom wall, then the left wall at a point well below the top edge, with a dashed horizontal normal at that red dot. At a vertical wall the leftward motion flips to rightward while the upward climb continues unchanged, so the ball now travels up and right at the same angle. The open q...
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In this last view, the final leg climbs from the left wall up and to the right, meeting the top edge at a red dot. That point lies just to the right of the divider between holes 1 and 2, so it falls inside hole 2, the middle hole. The ball therefore enters hole 2 first. Answer: 2.
train
mit
procedural_grid
13,535
S5.replay_unsupported
ecaaf08dd3ae272b
motif_ball_tracking
ball_tracking_naive
**Rules:** 1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion; 2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1; 3. The black boundaries of the image represent solid walls. When the ball hit...
null
2
1
1
I need to know which hole the ball enters first. The input shows the red ball in the upper-left of the box and the green arrow pointing up and slightly right, so the ball first moves straight toward the top edge. The arrow is too short to show where that line meets the top, so I cannot yet tell which opening it crosses...
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On my map, the straight line from the ball runs up and to the right and meets the top boundary at the red dot. That dot lies between the first divider and the second one, in the opening marked 2. Since the ball travels in a straight line from its start and no wall is hit before it reaches the top, it simply passes thro...
train
mit
procedural_grid
8,503
S5.replay_unsupported
a1576207287dd166
motif_ball_tracking
ball_tracking_naive
**Rules:** 1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion; 2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1; 3. The black boundaries of the image represent solid walls. When the ball hit...
null
4
1
3
The question asks which top hole the ball enters first. The input shows the red ball near the middle of the box with the green arrow pointing down-right, so the ball heads toward the lower-right area. All five holes are along the top, so the ball must bounce before reaching any of them, and the input alone does not sho...
The map shows the first path: from the ball it runs down-right and meets the bottom wall at a red dot left of the lower-right corner, with the blue dashed line standing vertically at the contact. So the first bounce is on the bottom wall, and since that wall is horizontal, the vertical part of the motion flips while th...
This picture shows the second segment leaving the bottom point up-right and meeting the right wall at a red dot well below the top edge, with the blue dashed line now horizontal. So the second bounce is on the right, vertical, wall: the horizontal part flips and the vertical part keeps going up, so the ball now travels...
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In this picture the third segment runs from the right-wall point up-left and crosses the top boundary at a red dot. That dot lies just to the right of the line separating holes 3 and 4, inside the span of hole 4, not in hole 3 or hole 5. Since the ball travels in a straight line until it enters a hole, and this crossin...
train
mit
procedural_grid
13,650
S5.replay_unsupported
22050902639b9010
motif_ball_tracking
ball_tracking_naive
**Rules:** 1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion; 2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1; 3. The black boundaries of the image represent solid walls. When the ball hit...
null
3
1
1
I need to find which numbered hole the ball enters first. The input shows a red ball in the lower-left region of the box with a green arrow pointing up and to the right at a fairly steep angle, and four holes labeled 1 to 4 along the top wall. The arrow only indicates direction; it does not show where that straight pat...
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On the map, the straight line from the ball runs up and to the right and meets the top boundary at the red dot. That dot sits inside the third cell, just left of the divider between holes 3 and 4 and well right of the divider between 2 and 3. Since the ball moves in a straight line at constant speed and this path reach...
train
mit
procedural_grid
8,607
S5.replay_unsupported
End of preview. Expand in Data Studio

Spatial MMCoT v1 · motif

MoTiF (OpenRaiser/MoTiF), the naive arm of its procedurally generated multi-step tasks: ball_tracking_naive, manipulation_naive, maze_naive (manipulation shows MoTiF's own CLEVR-style 3D renders of solids, not images from the CLEVR dataset). Each step has its own target image. The reflexion arm, which pairs each problem with a deliberately corrupted frame, is not included. sokoban_naive is excluded (7,997 upstream rows, S0.task_excluded): its eight numeric options are generated from the answer, so the correct option is the largest option minus 7 on almost every row, and the task can be answered from the option text without looking at the board. Manipulation can be partly answered without the image, in two ways: count questions ('how many ...') offer four consecutive integers and the correct count is never the largest of them, and for 'what is the object ...' questions the option named last in the operation list, and not in the question, is often right. Report manipulation scores next to the text-only baselines, with count questions scored separately (numbers under Known issues). VisWorld-Eval (thuml/VisWorld-Eval) ballgame uses the same rule text and question as ball_tracking_naive, so it is in-domain; VisWorld-Eval multihop asks the same kind of question as manipulation_naive (numbered place, swap, change and remove operations on CLEVR-style rendered scenes, then where an object is or which object is where); its wording is paraphrased and S11 found no shared images, so it is near-domain. Do not report either as out-of-distribution for a model trained on this source. Every read-back ends with a \boxed{} that holds the <answer> key (rows with no box were refused at conversion, S0.no_boxed_answer). On 12 rows upstream boxed the option's value instead of its key; that box was rewritten to the key (flag S0.boxed_value_to_key), so those read-backs are not verbatim.

Reasoning text in this release (r4)

The paragraph above describes the upstream data, and where it describes the reasoning text it describes the text of the previous release (r3). In this release every thought was rewritten: Qwen3.8-27B in thinking mode (temperature 1.0, top-p 0.95, top-k 20; prompt v4.1, scripts/annotate/rationale.py in our conversion code (the code repository is not public yet)) was shown the row's input images, its target images in order, the question, the options and the answer, and wrote the thought before each target image (what is still unknown, and what the picture should show to settle it) and the read-back after the last one. The images, the question, the options, the answer and the number of steps are r3's, checked row by row (image bytes, instruction, K and the <answer> value).

This is the training subset: 136 rows of r4 are not in it, listed with their reason in reports/subset_dropped.jsonl: 135 the rewrite model judged the stored answer doubtful (its note is in the list) (label_doubt); 1 no successful rewrite (R.no_rewrite).

Self-check of the rewritten text (measured 2026-10-02 on 22 rows sampled from this source before the removals above, each judged against its full-resolution pictures): 0.09 faithfulness errors per row (a claim the pictures contradict), 91% of rows with none; the plan names the real obstacle on 96%, the read-back reads the picture it follows on 100%, and the answer follows from the text on 100%.

The measured caveats on the r3 card were counted on r3's rows and text and are not repeated here; the per-row known-issue lists below were measured again on these rows and this text.

Supervision kind (supervision_kind in meta): full_interleaved on every row: the upstream trace itself interleaves text and target images (drawn or rendered states on most sources; the source note above says which), and the read-back comes after the target image it reads. In this release the text was rewritten by a model shown every image of the row (see the r4 section above).

Upstream: OpenRaiser/MoTiF. Licence: mit.

Known issues

Rows with a measured per-row problem are listed in reports/known_issues/, one TSV per issue (a # <description> line, then row_uid<TAB>split<TAB>detail lines), so they can be filtered out. They are still in this release: no row was removed for these issues.

issue rows train validation what how it was found file
count_options_give_answer 146 143 3 Count questions offer four consecutive integers and the correct count is never the largest; when the smallest option is above 0 the answer is always the second largest (options 1-4 mean 3, options 2-5 mean 4), so these rows can be answered from the options alone. task manipulation_naive, a 'how many' question whose four options are consecutive integers with the smallest above 0; measured 2026-10-03; known_issues.py sha1 b2249331; export b3fa1b9 rows 7e9d8e8b/95ff710a reports/known_issues/count_options_give_answer.tsv

To leave the listed rows out (the snippet in the loader section downloads reports/known_issues/ with the data):

import glob, os
root = "<root>/motif"
drop = {line.split("\t")[0] for f in glob.glob(os.path.join(root, "reports/known_issues/*.tsv"))
        for line in open(f) if line.strip() and not line.startswith(("#", "row_uid\t"))}
# keep a row when its row_uid (a column of train/, meta/ and preview/) is not in drop

Size

split rows target image slots distinct target images
train 20,298 42,902 42,870
validation 631 1,341 1,341

A slot is one target position in one row; rows can share a target image (same scene or same intermediate state), and a row can repeat one of its own targets, so there are fewer distinct images (by content hash) than slots.

task train validation
ball_tracking_naive 7,687 232
manipulation_naive 5,620 167
maze_naive 6,991 232

Input images per row: 1. Target images per row (the images the model is trained to generate): 1 to 4. Image corpus (source_scene_corpus): procedural_grid 15,142, blender_clevr 5,787. procedural_grid is this pipeline's label for any procedurally generated synthetic image (2D grid puzzles and simple 3D renders of primitive objects alike); the source note above says what the images show.

Row format

One row is: input image(s) and a question, then K rounds of thought → target image (the target is the source's own ground-truth image, which the model is trained to generate), then a final thought (normally a read-back of the last target; where a source's final thought is something else, or often leaves out the answer, the source note or Known issues says so) and the answer; here K is 1 to 4. In the train config:

image_list        list<binary>  inputs first, then the K target images in order
num_input_images  int64         how many of image_list are inputs
instruction_list  list<string>  one element: system prompt + question, + options on 5,787 of 20,929 rows
output_text_list  list<string>  K+1 elements:
  [0]   <think>plan 1</think><image_start>
  [j]   <image_end><think>plan j+1</think><image_start>
  [K]   <image_end><think>read-back</think><answer>answer</answer>
row_uid           string        join key to `meta` and `preview`

<answer> holds what the model is trained to emit. On 15,142 of 20,929 rows it equals meta.answer_value; on the other 5,787 (answer type mcq_letter 5,787) it holds the option key (a letter for mcq_letter), while meta.answer_value (the answer column of preview) holds that option's text. Map the key through the options listed in the question before comparing the two, and score model output against <answer>.

The system prompt is ThinkMorph's VLM_THINK_SYSTEM_PROMPT from its inferencer.py, verbatim (GEN_THINK_SYSTEM_PROMPT there has the same text), including its leading and trailing newline. The markers are plain strings, not tokenizer special tokens; the prompt writes </image_end> and the data writes <image_end>, exactly as the ThinkMorph-7B checkpoint was trained.

preview shows the same rows with one column per slot: input_image_i for the inputs; for each of the K = num_steps rounds, the plan thought_j and its target target_image_j, both empty for K <= j < 5; and the read-back in thought_5 on every row.

meta holds the per-row sidecar: task, scene_id and geometry_uid (the scene and geometry keys; the split key is named in the split paragraph below), trajectory_id (a camera-path or sample label, empty where the source has none), num_steps, num_input_images, answer_type, answer_value, majority_class_rate, target_image_kind, target_px, est_tokens, licence, split (train / validation, the Hub split names), supervision_kind (full_interleaved / visual_aux / visual_only) and filter_flags. majority_class_rate is the share of the task's most frequent answer_value among its training rows: it measures answer skew and is not a guessing baseline (where a task mixes question types or each row has its own options it can be far below chance); compare scores with the text-only baselines below.

Per-row license in meta: mit 20,929.

Flags on released rows (filter_flags in meta and preview, comma-separated):

flag rows meaning
S5.replay_unsupported 20,929 no solver re-derives this task's answer from the trace, so S5 did not replay it
S8.phash_near_but_distinct 10,205 a target's perceptual hash is within 6 bits of an input image's, but its pixels differ, so it is not a copy; kept
S14.sampled_qa 199 chosen for the S14 human spot-check (reports/s14_sample.tsv)
S0.boxed_value_to_key 12 upstream boxed the option's value; the read-back's \boxed{} was rewritten to the option key
S0.row_uid_salted 3 the content-derived row_uid repeated within the build and was re-derived

Training with a BAGEL-family loader

Every row here has one input image (num_input_images is 1), so the stock ThinkMorph UnifiedEditIterableDataset (https://github.com/ThinkMorph/ThinkMorph: image_list[0] as input, image_list[j+1] after output_text_list[j]) and the IPT release's version (which reads num_input_images) both read it as intended. Mixed with a source whose rows have more than one input image, only a loader that reads num_input_images is correct.

The stock BAGEL edit loader (ByteDance-Seed/Bagel) cannot train these rows: it never reads output_text_list and expects each instruction_list element to be a list of paraphrases.

parquet_info.json keys each training chunk as <source>/<split>/<file>, here motif/train/chunk_00000.parquet, with row-group counts read from the parquet footers. The loader matches a chunk only when its key equals the path it builds, os.path.join(data_dir, file), and skips a chunk with no key without a warning: a source that is alone in its group then fails with IndexError: list index out of range, and in a mixed group it adds no rows. Download into a directory named after the source, not after the repository:

from huggingface_hub import snapshot_download
snapshot_download("yrlyrl/spatial-mmcot-motif", repo_type="dataset", local_dir="<root>/motif",
                  allow_patterns=["train/*", "validation/*", "parquet_info.json", "reports/known_issues/*"])

Then either run from <root> with data_dir: motif/train and parquet_info_path: motif/parquet_info.json, or rebuild the index with absolute keys and use an absolute data_dir:

import json, os
root = "/abs/path/to/root"                      # the directory that holds motif/
info = json.load(open(os.path.join(root, "motif", "parquet_info.json")))
info = {os.path.join(root, k): v for k, v in info.items()}
json.dump(info, open(os.path.join(root, "motif", "parquet_info_abs.json"), "w"))
# data_dir = os.path.join(root, "motif", "train")   (spelled exactly so, no trailing slash)
# parquet_info_path = os.path.join(root, "motif", "parquet_info_abs.json")

The Hugging Face cache (.../snapshots/<hash>/train/) or a folder named spatial-mmcot-motif matches no key.

num_used_data counts chunk files, not rows: the loader repeats this source's file list up to that number, lists every (file, row group) pair, and deals whole row groups out, floor(R / world_size) to each rank and floor(that / num_workers) to each DataLoader worker. The remainder is never read. This source has 1 training chunk file holding 159 row groups of up to 128 rows, so keep num_used_data large, e.g. the 128 of ThinkMorph's interleaved_reasoning.yaml (upstream's example.yaml asks for more than GPUs x workers); every row group is then read. Set to 1 and alone in its group on 8 GPUs with 4 workers, it reads only 128 of the 159 row groups. In a run that mixes sources, give each source the same multiple of its own training chunk-file count, e.g. 128 per file (128 here): the file list is repeated up to num_used_data entries, so a flat 128 for every source would read a two-file source's rows half as often as a one-file source's.

How the rows were chosen

stage rows
upstream rows read 31,362
refused before conversion (S0raw; each reason is in the table below) 8,092
quarantined at S4c (an automatic check could not match the read-back's conclusion to the label) 2,094
dropped at S5 (the text contains a phrase from S5's self-contradiction list, e.g. 'does not make sense', 'discrepancy', 'there must be a mistake'; a keyword match, not a comparison with the images, so it also removes some sound rows) 37
dropped at S8 (a target was removed as a copy of an input, as transparent or as too small, and the row had no target left or was a multi-step chain that cannot lose a state) 70
after conversion and per-row filters 21,069
removed by S10 (3 exact duplicates; 1 near duplicate) 4
removed by answer-prior balancing (S13) 0
removed for training after the r4 rewrite (subset_dropped.jsonl) 136
released 20,929

Every removed row has one line, with its reason, in reports/:

file step reason (the line's flag, or the field shown) rows
build/dropped.jsonl S0raw S0.task_excluded 7,997
build/dropped.jsonl S0raw S0.no_boxed_answer 95
build/dropped.jsonl S5 S5.self_contradiction 37
build/dropped.jsonl S8 S8.chain_broken 70
build/quarantine.jsonl S4c S4c.cot_label_conflict 2,094
s10_dropped.jsonl S10 level: exact 3
s10_dropped.jsonl S10 level: near 1
subset_dropped.jsonl r4 reason: label_doubt 135
subset_dropped.jsonl r4 reason: R.no_rewrite 1

S0raw lines in build/dropped.jsonl were refused before a release row existed, so their row_uid field holds the converter's key for the upstream record, not a 16-hex row_uid; lines from later steps carry the row_uid the row had. No removed row appears in meta or preview. For this source the key is built from upstream fields that repeat across rows (for most sources a hash of the question text), so it is not unique: the 95 S0.no_boxed_answer lines carry 22 distinct keys; the 7,997 S0.task_excluded lines carry 7,949 distinct keys. Those rows are counted with their reason but cannot be traced to individual upstream rows.

2,094 rows were quarantined rather than dropped (S4c): an automatic check could not match the read-back's stated conclusion to the stored label. They were not reviewed by hand, and some are phrasing mismatches rather than wrong labels.

S8.k_zero and S8.chain_broken name what happened to the row, not which check removed the image; the lines in this build do not record whether it was the size, transparency or copy check.

Per-step counters of the conversion

31,362 upstream rows were read; S0raw refused 8,092 before a row existed and passed 23,270 to the first step. S0 runs once more, last, on the final bytes. The reason for every refused, dropped or quarantined row is in the files above.

step in out dropped quarantined rejected repaired
S0raw (refused before conversion) 31,362 23,270 0 0 8,092 0
S4 23,270 23,270 0 0 0 0
S4c 23,270 21,176 0 2,094 0 0
S5 21,176 21,139 37 0 0 0
S8 21,139 21,069 70 0 0 0
S9 21,069 21,069 0 0 0 0
S0 (final structural check, after S9) 21,069 21,069 0 0 0 0

The train/validation split keeps rows sharing a scene_id in meta on one side, and the assignment is frozen (splits/ in the summary repository). MoTiF has no scene ids: scene_id is the md5 of the upstream input image, so a key is one puzzle's starting image. S12 saw 21,065 rows under 21,040 keys; 17 rows joined another key because they share an input image. No validation input image has the content of a training input image. The S12 run did not record whether its pixel-level near-copy test ran for this source, so near-copies are not ruled out. Target images are not covered by that check: 1 target-image slot in validation rows holds an image with the same content as a training target image (S12 compares a 64x64 greyscale hash and counts slots, so an image repeated in validation counts each time). These are states that other puzzles also reach, as a step or as their final state.

Answer-prior balancing (S13)

Each (task, split) group is checked separately. An answer is the answer value compared as lower-cased text without a trailing full stop, with 'farther' read as 'further' and 'nearer' as 'closer' (for multiple choice, the option text, not the letter; where the candidates are drawn in the image, as in zebra_jigsaw and zebra_tetris, the answer is the letter itself). An answer is real when it holds at least 5 rows and 2% of the group; k is the number of real answers. Answer step: the target is max(30%, 1/k) when k >= 2, and max(30%, 1/d) over the d distinct answers when k = 1; a validation group uses the larger of its own target and its task's train target. A group is cut only when k >= 1 and its most common answer holds more than the target plus 5 percentage points; every answer is then capped at one common count, chosen so that none exceeds the target, and smaller answers keep all their rows. At the answer step, a group at or below that trigger, or with no real answer (k = 0), is left as it is, so its most common answer can hold up to the target plus 5 percentage points. A task whose train group has exactly two real answers is instead cut, in every split, so that its two largest answers have equal counts, with no trigger. Rank and label steps: then, in a group where every option value of every row is a number, the rank of the correct option among the sorted values, and after it, in a group where every trained answer is an option label, the label, are each capped by the same cut-and-trigger rule on their own counts (own target, validation included): capped, never evened out, so two labels are cut only when one exceeds 55%, and then only down to 50%. These steps can also cut groups the answer step left whole, including k = 0 groups, and can raise an answer's final share above its target; the run fails if a real answer ends above the target plus 5 percentage points. A train group of at least 20 rows in which one answer holds 90% or more fails the run. PET (exact_cells_pet) instead cuts each (question type x turn direction) cell to equal counts of its two answers; a PET cell that shows only one answer is removed.

task split pass rule rows in → out real answers k target largest share, before → after cut
ball_tracking_naive train answer cap30[canon] 7,753 → 7,753 5 30.0% 28.6% → 28.6% no
ball_tracking_naive validation answer cap30[canon] 232 → 232 5 30.0% 32.8% → 32.8% no
manipulation_naive train answer cap30[canon] 5,629 → 5,629 26 30.0% 13.8% → 13.8% no
manipulation_naive train letter cap30[letter] 5,629 → 5,629 4 30.0% 26.5% → 26.5% no
manipulation_naive validation answer cap30[canon] 168 → 168 17 30.0% 8.3% → 8.3% no
manipulation_naive validation letter cap30[letter] 168 → 168 4 30.0% 29.2% → 29.2% no
maze_naive train answer cap30[canon] 7,047 → 7,047 11 30.0% 13.8% → 13.8% no
maze_naive validation answer cap30[canon] 236 → 236 10 30.0% 14.8% → 14.8% no

S13 removed no row from this source.

Text-only baselines

Accuracy of guessers that never see an image. For each task the released training rows are split into two fixed halves by a hash of row_uid; each guesser is fitted on one half and scored once on the other (one held-out half, not cross-validation; eval rows below). The reference is chance (the mean of 1 / number of options) where every row is multiple choice, and otherwise the eval-half accuracy of always giving the answer most common in the fit half (when a task's top answers are nearly tied, this need not be the task's most common answer; the line after the table gives that answer's validation score). Accuracies are recounted from the stored rates and eval rows, so they are exact. A task is flagged when a text-only guesser beats its reference by more than 0.15 (for a free-form task, a guesser other than the most common answer). A flagged task can be partly answered from the text alone; an unflagged task passed only these probes, which do not prove the text carries no answer. Report scores on every task next to this baseline.

Guessers: keywords: the most common answer per set of spatial words in the question; last_mentioned: the option named last in the question body; letter_prior: the most common answer letter; majority: the answer most common in the fit half; numeric_offset: where every option is a number, the smallest or largest option plus or minus the offset the correct one sat at most often (last_mentioned on the other rows); option_prior: the option text that won most often when shown; option_rank: where every option is a number, the option at the rank among the sorted values that the correct one held most often (last_mentioned on the other rows); template: the most common answer per question wording (numbers masked, object names kept).

task best text-only guesser accuracy reference margin eval rows flagged
ball_tracking_naive keywords 0.249 0.249 (majority) +0.000 3,888 no
manipulation_naive option_rank, rank 1 (0 = smallest) on the 842 numeric-option eval rows; last_mentioned on the other 1925; 0.448 on the 842 numeric-option rows 0.467 0.250 (chance) +0.217 2,767 yes
maze_naive keywords 0.127 0.127 (majority) +0.000 3,536 no

Always giving the most common training answer, scored on the validation split (the constant baseline to compare validation scores with): ball_tracking_naive: always answering 1 (28.7% of training rows) scores 0.328 (76/232); maze_naive: always answering 5 (13.8% of training rows) scores 0.116 (27/232).

For manipulation_naive the count questions alone can be answered from the option list far better than the pooled numbers above show (see Known issues); S13's rank step did not run on them, because the group mixes numeric and object options.

Spot-check (S14)

Pending. The S14 rows are chosen and flagged S14.sampled_qa in meta and preview; the human pass over them has not been signed off yet.

Citation

MoTiF's card gives no citation. Please credit the repository, OpenRaiser/MoTiF (MIT).

Provenance

The release files were written by our conversion code (the code repository is not public yet), scripts/convert/export.py at commit b3fa1b993ca9, from build motif_r3. The build was made by scripts/convert/run_source.py from the same repository at commit 76c78bd817c2. S10, S12 and S13 ran before the export; reports/export_manifest.json pins every input the export read by SHA-1 (build_manifest_sha1, s10_keep_sha1, s12_assignments_sha1, s13_balanced_keep_sha1).

Every row removed between upstream and this release has one line, with its reason, in reports/: build/dropped.jsonl (rows refused before conversion or dropped by a conversion step); build/quarantine.jsonl (rows set aside by S4c because an automatic check could not match the read-back's conclusion to the label); s10_dropped.jsonl (duplicates removed by S10); s10_label_conflicts.jsonl (rows S10 withheld because another row asks the identical question, options in the same order, of the same images with a different answer); s13_dropped.jsonl (rows removed by answer-prior balancing). known_issues/ lists rows with a measured problem (see Known issues); reports/ also holds the build manifest (absolute paths cut to basenames) and counters, the S14 sample list (s14_sample.tsv: row_uid, task, split) and export_manifest.json. In reports/build/manifest.json, spec.source_scene_corpus (procedural_grid) is only the converter's fallback for rows that carry no corpus of their own; it does not describe every row. Each row's corpus is source_scene_corpus in meta (procedural_grid 15,142, blender_clevr 5,787). Part of yrlyrl/spatial-mmcot.

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