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332 | [{"role": "user", "question": "A path $D E F B$ with $D E \\perp E F$ and $E F \\perp F B$ lies within the square $A B C D$ as shown. We know that $D E=5, E F=1$ and $F B=2$. What is the side length of the square?\n<image1>", "hint": "", "options": {"A": "$3 \\sqrt{2}$", "B": "$\\frac{7 \\sqrt{2}}{2}$", "C": "$\\frac{1... | E | mcq | 5 | metric geometry - length | |
333 | [{"role": "user", "question": "Three circles with radius 2 are drawn in such a way that each time one of the points of intersection of two circles is identical with the centre of the third circle. How big is the area of the grey zone?\n<image1>", "hint": "", "options": {"A": "$\\pi$", "B": "$3 \\pi$", "C": "$\\frac{\\p... | D | mcq | 5 | metric geometry - area | |
334 | [{"role": "user", "question": "Numbers are to be placed into the square grid shown, so that each of the numbers $1,2,3,4$ and 5 appears exactly once in each row and in each column. Furthermore sthe sum of all numbers in the three black-bordered sections should always be the same. Which number has to be written into the... | 3 | numeric | 1 | logic | |
335 | [{"role": "user", "question": "An ant walked $6 \\mathrm{~m}$ every day to go from point $A$ to point $B$ in a straight line. One day Johnny put a straight cylinder of one meter high in that way. Now the ant walks on the same straight line or above it, having to go up and down the cylinder, as shown in the picture. How... | A | mcq | 3 | solid geometry | |
336 | [{"role": "user", "question": "The pie chart beside refers to the number of inhabitants of the five zones of a city. The central zone has the same population as the north, west and east zones together and the south zone has half of the inhabitants of the west zone. What is the percentage difference between the inhabita... | D | mcq | 3 | statistics | |
337 | [{"role": "user", "question": "In the addition on the right, different letters represent different numbers. Assuming the account is correct, what is the highest possible value for the sum $\\mathrm{C}+\\mathrm{A}+\\mathrm{N}$?\n<image1>", "hint": "", "options": {}, "choices": []}] | 21 | numeric | 5 | algebra | |
338 | [{"role": "user", "question": "A gray square with an area of $36 \\mathrm{~cm}^{2}$ and a black square with an area of $25 \\mathrm{~cm}^{2}$ are superimposed, as shown beside. What is the perimeter of the overlapping region, represented by the white quadrilateral, which has a vertex on the side of the gray square?\n<i... | D | mcq | 5 | metric geometry - length | |
339 | [{"role": "user", "question": "Zilda will use six equal cubes and two different rectangular blocks to form the structure beside with eight faces. Before gluing the pieces, she will paint each one entirely and calculated that she will need 18 liters of paint (the color does not matter). How many liters of paint would sh... | 11.5 | numeric | 3 | solid geometry | |
34 | [{"role": "user", "question": "Max has cut a rectangle into two pieces. One piece looks like:\n<image1>\nWhat does the other piece look like?\n<image2>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | E | mcq | 1 | combinatorial geometry | |
340 | [{"role": "user", "question": "The last two digits of a 2020 number are 9 and 9. At most, how many digits does the square of that number have?\n<image1>", "hint": "", "options": {}, "choices": []}] | 4040 | numeric | 5 | algebra | |
341 | [{"role": "user", "question": "Matias wrote 15 numbers on the wheel represented beside. Only one of them is visible, the 10 on top of the wheel. The sum of the numbers in any seven consecutive positions, such as the gray positions in the figure, does not vary. When seven numbers in consecutive positions are summed up, ... | B | mcq | 1 | logic | |
342 | [{"role": "user", "question": "A large square touches another two squares, as shown in the picture. The numbers inside the smaller squares indicate their areas. What is the area of the largest square?\n<image1>", "hint": "", "options": {}, "choices": []}] | 13 | numeric | 5 | metric geometry - area | |
343 | [{"role": "user", "question": "A circle is tangent to one side of a rectangle and passes through two of its vertices, as shown beside. A square of $20 \\mathrm{~cm}^{2}$ area has one side over the side of the rectangle and two vertices over the circle, as shown in the figure. What is the area of the rectangle?\n<image1... | C | mcq | 5 | metric geometry - area | |
344 | [{"role": "user", "question": "Two rectangular blocks and a cube are joined to form a larger rectangular block, which volume is $280 \\mathrm{~cm}^{3}$. The cube, in dark gray in the picture, has volume equal to $125 \\mathrm{~cm}^{3}$ and the smaller rectangular block has volume equal to $75 \\mathrm{~cm}^{3}$. What i... | A | mcq | 3 | solid geometry | |
345 | [{"role": "user", "question": "The figure shows the lines $r$ and $s$, which equations are, respectively, $y=a x\n+b$ e $y=c x+d$. Which of the following statements is true?\n<image1>", "hint": "", "options": {"A": "$a b+c d<0$", "B": "$a+b+c+d<0$", "C": "$a c+b d \\geq 0$", "D": "$a+b+c+d>0$", "E": "$a b c d>0$"}, "ch... | A | mcq | 4 | analytic geometry | |
346 | [{"role": "user", "question": "A little kangaroo draws a line passing through point $P$ of the grid and then paints three triangles in black as shown in the picture. The areas of these triangles are proportional to which numbers?\n<image1>", "hint": "", "options": {"A": "$1: 4: 9$", "B": "$1: 2: 9$", "C": "$1: 3: 9$", ... | A | mcq | 4 | analytic geometry | |
347 | [{"role": "user", "question": "A rectangular garden was $50 \\mathrm{~m}$ long and $40 \\mathrm{~m}$ wide. An artificial lake was built next to it, so that the whole set forms a $60 \\mathrm{~m}$ square. Then a fence was stretched, separating both the garden and the lake in two parts with equal areas, as shown in the p... | B | mcq | 5 | metric geometry - length | |
348 | [{"role": "user", "question": "Vilma took a sheet of paper measuring $10 \\mathrm{~cm} \\times 20 \\mathrm{~cm}$ and made two folds, taking the two smaller sides of the sheet to a diagonal of it. She gets a parallelogram, as shown in the picture. What is the area of this quadrilateral, in $\\mathrm{cm}^{2}$?\n<image1>"... | D | mcq | 5 | transformation geometry | |
349 | [{"role": "user", "question": "There are $n$ different prime numbers $p_{1}, p_{2}, \\ldots, p_{n}$ written from left to right on the last line below the table shown beside. The product of two neighboring numbers in the same line is written in the upper two boxes. The number $K=p_{1}^{\\alpha_{1}} \\cdot p_{2}^{\\alpha... | 28 | numeric | 5 | algebra | |
35 | [{"role": "user", "question": "Seven sticks lay on top of each other. Stick 2 lays right at the bottom. Stick 6 lays right on top. Which stick lays exactly in the middle?\n<image1>", "hint": "", "options": {}, "choices": []}] | 3 | numeric | 2 | descriptive geometry | |
350 | [{"role": "user", "question": "Adam and Bruna try to find out which is Carla's favorite figure, amongst the figures beside. Adam knows that Carla told Bruna what the shape of the figure was. Bruna knows that Carla told Adam what color the figure was. The following conversation takes place. Adam: \"I don't know what Car... | E | mcq | 1 | logic | |
351 | [{"role": "user", "question": "Paula's weather app shows a diagram of the predicted weather and maximum temperatures for the next seven days, as shown. Which of the following represents the corresponding graph of maximum temperatures?\n<image1>\n<image2>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D",... | E | mcq | 3 | statistics | |
352 | [{"role": "user", "question": "A large square is divided into smaller squares, as shown. A shaded circle is inscribed inside each of the smaller squares. What proportion of the area of the large square is shaded?\n<image1>", "hint": "", "options": {"A": "$\\frac{8 \\pi}{9}$", "B": "$\\frac{13 \\pi}{16}$", "C": "$\\frac... | E | mcq | 5 | metric geometry - area | |
353 | [{"role": "user", "question": "After the storm last night, the flagpole on our school building is leaning over. Looking from northwest, its tip is to the right of its bottom point. Looking from the east, its tip is also to the right of its bottom point. In which direction could the flagpole be leaning over?\n<image1>",... | A | mcq | 1 | descriptive geometry | |
354 | [{"role": "user", "question": "The parabola in the figure has an equation of the form $y=a x^{2}+b x+c$ for some distinct real numbers $a, b$ and $c$. Which of the following equations could be an equation of the line in the figure?\n<image1>", "hint": "", "options": {"A": "$y=b x+c$", "B": "$y=c x+b$", "C": "$y=a x+b$"... | D | mcq | 4 | analytic geometry | |
355 | [{"role": "user", "question": "A large triangle is divided into smaller triangles as shown. The number inside each small triangle indicates its perimeter. What is the perimeter of the large\ntriangle?\n<image1>", "hint": "", "options": {}, "choices": []}] | 34 | numeric | 5 | metric geometry - length | |
356 | [{"role": "user", "question": "In the $5 \\times 5$ square shown the sum of the numbers in each row and in each column is the same. There is a number in every cell, but some of the numbers are not shown. What is the number in the cell marked with a question mark?\n<image1>", "hint": "", "options": {}, "choices": []}] | 10 | numeric | 1 | logic | |
357 | [{"role": "user", "question": "A piece of string is lying on the table. It is partially covered by three coins as seen in the figure. Under each coin the string is equally likely to pass over itself like this: <image1>\nor like this: <image2>. What is the probability that the string is knotted after its ends are pulled... | B | mcq | 1 | topology | |
358 | [{"role": "user", "question": "A naughty pup grabs the end of a roll of toilet paper and walks away at a constant speed. Which of the functions below best describes the thickness $y$ of the roll as a function of the unrolled part $x$?\n<image1>\n<image2>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D",... | E | mcq | 4 | analytic geometry | |
359 | [{"role": "user", "question": "The diagram shows three squares, $P Q R S, T U V R$ and $U W X Y$. They are placed together, edge to edge. Points $P, T$ and $X$ lie on the same straight line. The area of $P Q R S$ is 36 and the area of TUVR is 16. What is the area of triangle PXV?\n<image1>", "hint": "", "options": {}, ... | 16 | numeric | 5 | metric geometry - area | |
36 | [{"role": "user", "question": "The rabbit family Hoppel eat cabbages and carrots. Each day they eat either 10 carrots or 2 cabbages. In the whole of last week they ate 6 cabbages. How many carrots did the rabbit family eat last week?\n<image1>", "hint": "", "options": {}, "choices": []}] | 40 | numeric | 2 | arithmetic | |
360 | [{"role": "user", "question": "The figure shows the graph of a function $f:[-5,5] \\rightarrow R$. How many distinct solutions does the equation $f(f(x))=0$ have?\n<image1>", "hint": "", "options": {}, "choices": []}] | 8 | numeric | 4 | analytic geometry | |
361 | [{"role": "user", "question": "Five kangaroos named A, B, C, D and E have one child each, named a, b, c, d and e, not necessarily in that order. In the first group photo shown exactly 2 of the children are standing next to their mothers. In the second group photo exactly 3 of the children are standing next to their mot... | D | mcq | 1 | logic | |
362 | [{"role": "user", "question": "The solid shown in the diagram has 12 regular pentagonal faces, the other faces being either equilateral triangles or squares. Each pentagonal face is surrounded by 5 square faces and each triangular face is surrounded by 3 square faces. John writes 1 on each triangular face, 5 on each pe... | 50 | numeric | 3 | solid geometry | |
363 | [{"role": "user", "question": "On a circle 15 points are equally spaced. We can form triangles by joining any 3 of these. Congruent triangles, by rotation or reflection, are counted as only one triangle. How many different triangles can be drawn?\n<image1>", "hint": "", "options": {}, "choices": []}] | 19 | numeric | 5 | combinatorics | |
364 | [{"role": "user", "question": "A triangle $A B C$ is divided into four parts by two straight lines, as shown. The areas of the smaller triangles are 1,3 and 3. What is the area of the original triangle?\n<image1>", "hint": "", "options": {}, "choices": []}] | 12 | numeric | 5 | metric geometry - area | |
365 | [{"role": "user", "question": "Two plane mirrors $O P$ and $O Q$ are inclined at an acute angle (diagram is not to scale). A ray of light $X Y$ parallel to $O Q$ strikes mirror $O P$ at $Y$. The ray is reflected and hits mirror $O Q$, is reflected again and hits mirror $O P$ and is reflected for a third time and strike... | C | mcq | 5 | metric geometry - length | |
366 | [{"role": "user", "question": "Martin's smartphone displays the diagram on the right. It shows how long he has worked with four different apps in the previous week. The apps are sorted from top to bottom according to the amount of time they have been used. This week he has spent only half the amount of time using two o... | E | mcq | 3 | statistics | |
367 | [{"role": "user", "question": "Four circles with radius 1 intersect each other as seen in the diagram. What is the perimeter of the grey area?\n<image1>", "hint": "", "options": {"A": "$\\pi$", "B": "$\\frac{3 \\pi}{2}$", "C": "a number between $\\frac{3 \\pi}{2}$ and $2 \\pi$", "D": "$2 \\pi$", "E": "$\\pi^{2}$"}, "ch... | D | mcq | 5 | metric geometry - length | |
368 | [{"role": "user", "question": "The points $A, B, C$ and $D$ are marked on a straight line in this order as shown in the diagram. We know that $A$ is $12 \\mathrm{~cm}$ from $C$ and that $B$ is $18 \\mathrm{~cm}$ from $D$. How far apart from each other are the midpoints of the line segments $A B$ and $C D$?\n<image1>", ... | E | mcq | 5 | metric geometry - length | |
369 | [{"role": "user", "question": "Four straight lines that intersect in one single point form eight equal angles (see diagram). Which one of the black arcs has the same length as the circumference of the little (grey) circle?\n<image1>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices":... | D | mcq | 5 | metric geometry - length | |
37 | [{"role": "user", "question": "A square is cut into four pieces. Which shape can you not make with these four pieces?\n<image1>\n<image2>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | D | mcq | 1 | combinatorial geometry | |
370 | [{"role": "user", "question": "We check the water meter and see that all digits on the display are different. What is the minimum amount of water that has to be used before this happens again?\n<image1>", "hint": "", "options": {"A": "$0.006 \\mathrm{~m}^{3}$", "B": "$0.034 \\mathrm{~m}^{3}$", "C": "$0.086 \\mathrm{~m}... | D | mcq | 1 | arithmetic | |
371 | [{"role": "user", "question": "The square pictured, is split into two squares and two rectangles. The vertices of the shaded quadrilateral with area 3 are the midpoints of the sides of the smaller squares. What is the area of the non-shaded part of the big square?\n<image1>", "hint": "", "options": {}, "choices": []}] | 21 | numeric | 5 | metric geometry - area | |
372 | [{"role": "user", "question": "The diagram shows a map with 16 towns which are connected via roads. The government is planning to build power plants in some towns. Each power plant can generate enough electricity for the town in which it stands as well as for its immediate neighbouring towns (i.e. towns that can be rea... | 4 | numeric | 5 | graph theory | |
373 | [{"role": "user", "question": "A cuboid with surface area $X$ is cut up along six planes parallel to the sides (see diagram). What is the total surface area of all 27 thus created solids?\n<image1>", "hint": "", "options": {"A": "$X$", "B": "$2 X$", "C": "$3 X$", "D": "$4 X$", "E": "It depends on the position of the pl... | C | mcq | 3 | solid geometry | |
374 | [{"role": "user", "question": "A circle with midpoint $(0 \\mid 0)$ has a radius of 5. How many points are there on the circumference where both co-ordinates are integers?\n<image1>", "hint": "", "options": {}, "choices": []}] | 12 | numeric | 4 | analytic geometry | |
375 | [{"role": "user", "question": "Which two building blocks can be joined together so that the object shown is created?\n<image1>\n<image2>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | A | mcq | 5 | combinatorial geometry | |
376 | [{"role": "user", "question": "A rectangle is split into 11 smaller rectangles as shown. All 11 small rectangles are similar to the initial rectangle. The smallest rectangles are aligned like the original rectangle (see diagram). The lower sides of the smallest rectangles have length 1. How big is the perimeter of the ... | 30 | numeric | 5 | metric geometry - length | |
377 | [{"role": "user", "question": "Two rectangles are inscribed into a triangle as shown in the diagram. The dimensions of the rectangles are $1 \\times 5$ and $2 \\times 3$ respectively. How big is the height of the triangle in $A$?\n<image1>", "hint": "", "options": {"A": "3", "B": "$\\frac{7}{2}$", "C": "$\\frac{8}{3}$"... | B | mcq | 5 | metric geometry - length | |
378 | [{"role": "user", "question": "The numbers 1 to 10 were written into the ten circles in the pattern shown in the picture. The sum of the four numbers in the left and the right column is 24 each and the sum of the three numbers in the bottom row is 25. Which number is in the circle with the question mark?\n<image1>", "h... | E | mcq | 5 | algebra | |
379 | [{"role": "user", "question": "A square is placed in a co-ordinate system as shown. Each point $(x \\mid y)$ of the square is deleted and replaced by the point $\\left(\\frac{1}{x} \\mid \\frac{1}{y}\\right)$. Which diagram shows the resulting shape?\n<image1>\n<image2>", "hint": "", "options": {"A": "A", "B": "B", "C"... | C | mcq | 4 | analytic geometry | |
38 | [{"role": "user", "question": "Each of the digits 2, 3, 4 and 5 will be placed in a square. Then there will be two numbers, which will be added together. What is the biggest number that they could make?\n<image1>", "hint": "", "options": {}, "choices": []}] | 95 | numeric | 2 | arithmetic | |
380 | [{"role": "user", "question": "Two circles intersect a rectangle AFMG as shown in the diagram. The line segments along the long side of the rectangle that are outside the circles have length $A B=8, C D=26, E F=22, G H=12$ and $J K=24$. How long is the length $x$ of the line segment $L M$?\n<image1>", "hint": "", "opti... | 16 | numeric | 5 | metric geometry - length | |
381 | [{"role": "user", "question": "A cylindrical tin is $15 \\mathrm{~cm}$ high. The circumference of the base circle is $30 \\mathrm{~cm}$. An ant walks from point $A$ at the base to point $B$ at the top. Its path is partly vertically upwards and partly along horizontal circular arcs. Its path is drawn in bold on the diag... | E | mcq | 3 | solid geometry | |
382 | [{"role": "user", "question": "Emma should colour in the three strips of the flag shown. She has four colours available. She can only use one colour for each strip and immediately adjacent strips are not to be of the same colour. How many different ways are there for her to colour in the flag? <image1>", "hint": "", "o... | 36 | numeric | 5 | graph theory | |
383 | [{"role": "user", "question": "What is the value of the following sum? <image1>", "hint": "", "options": {}, "choices": []}] | 12 | numeric | 1 | arithmetic | |
384 | [{"role": "user", "question": "A square with area 84 is split into four squares. The upper left square is coloured in black. The lower right square is again split into four squares and so on. The process is repeated infinitely many times. How big is the area coloured in black? <image1>", "hint": "", "options": {}, "cho... | 28 | numeric | 5 | algebra | |
385 | [{"role": "user", "question": "The numbers from 1 to 9 are to be distributed to the nine squares in the diagram according to the following rules: There is to be one number in each square. The sum of three adjacent numbers is always a multiple of 3 . The numbers 7 and 9 are already written in. How many ways are there to... | 24 | numeric | 5 | combinatorics | |
386 | [{"role": "user", "question": "Two equilateral triangles of different sizes are placed on top of each other so that a hexagon is formed on the inside whose opposite sides are parallel. Four of the side lengths of the hexagon are stated in the diagram. How big is the perimeter of the hexagon? <image1>", "hint": "", "opt... | 70 | numeric | 5 | metric geometry - length | |
387 | [{"role": "user", "question": "In a three-sided pyramid all side lengths are integers. Four of the side lengths can be seen in the diagram. What is the sum of the two remaining side lengths? <image1>", "hint": "", "options": {}, "choices": []}] | 11 | numeric | 3 | solid geometry | |
388 | [{"role": "user", "question": "Leon has drawn a closed path on the surface of a cuboid. Which net can represent his path?\n<image1>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | D | mcq | 1 | descriptive geometry | |
389 | [{"role": "user", "question": "A pentagon is cut into smaller parts as shown in the diagram. The numbers in the triangles state the area of the according triangle. How big is the area $P$ of the grey quadrilateral? <image1>", "hint": "", "options": {}, "choices": []}] | 16 | numeric | 5 | metric geometry - area | |
39 | [{"role": "user", "question": "Ingrid has 4 red, 3 blue, 2 green and 1 yellow cube. She uses them to build the following object:\n<image1>\nCubes with the same colour don't touch each other. Which colour is the cube with the question mark?", "hint": "", "options": {"A": "red", "B": "blue", "C": "green", "D": "Yellow", ... | A | mcq | 3 | logic | |
390 | [{"role": "user", "question": "The diagram shows a spiral of consecutive numbers starting with 1. In which order will the numbers 625, 626 and 627 appear in the spiral? <image1>", "hint": "", "options": {"A": "$625 \\uparrow 626 \\uparrow 627$", "B": "$625 \\uparrow 626 \\rightarrow$", "C": "$625 \\rightarrow 626 \\rig... | B | mcq | 5 | algebra | |
391 | [{"role": "user", "question": "A game marker in the shape of a regular tetrahedron has one marked area. That side is placed on the triangle marked START. The marker is then moved within the diagram always to the next adjacent triangle by rolling it around an edge. On which triangle is the marker when it is on the marke... | E | mcq | 3 | solid geometry | |
392 | [{"role": "user", "question": "A part of a polynomial of degree five is illegible due to an ink stain. It is known that all zeros of the polynomial are integers. What is the highest power of $x-1$ that divides this polynomial? <image1>", "hint": "", "options": {"A": "$(x-1)^{1}$", "B": "$(x-1)^{2}$", "C": "$(x-1)^{3}$"... | D | mcq | 5 | algebra | |
393 | [{"role": "user", "question": "The big square shown is split into four small squares. The circle touches the right side of the square in its midpoint. How big is the side length of the big square? (Hint: The diagram is not drawn to scale.) <image1>", "hint": "", "options": {"A": "$18 \\mathrm{~cm}$", "B": "$20 \\mathrm... | A | mcq | 5 | metric geometry - length | |
394 | [{"role": "user", "question": "The numbers from 1 to 11 are written in the empty hexagons. The sums of the three numbers in three hexagons with a common bold point are always equal. Three of the eleven numbers are already written in (see diagram). Which number is written in the hexagon with the question mark? <image1>"... | 9 | numeric | 1 | logic | |
395 | [{"role": "user", "question": "Two identical cylindrical glasses contain the same amount of water. The left glass is upright, while the right one rests against the other one at a slant. The water level in both glasses is at the same height. The water level in the leaning glass touches its bottom in exactly one point (s... | A | mcq | 5 | metric geometry - area | |
396 | [{"role": "user", "question": "There are 10 boxes in the first van. Every further van contains twice as many boxes as the previous one. How many boxes are there in the fifth van?\n<image1>", "hint": "", "options": {}, "choices": []}] | 160 | numeric | 2 | algebra | |
397 | [{"role": "user", "question": "In the picture the distance $KM=10, LN=15, KN=22$. Find the distance $LM$.\n<image1>", "hint": "", "options": {}, "choices": []}] | 3 | numeric | 3 | metric geometry - length | |
398 | [{"role": "user", "question": "Chris constructed the brick on the picture using red and blue cubes of the same size. The outside of the brick is completely red, but all cubes used inside are blue. How many blue cubes did Chris use?\n<image1>", "hint": "", "options": {}, "choices": []}] | 12 | numeric | 5 | solid geometry | |
399 | [{"role": "user", "question": "This table shows the quantity of different types of flowers in the botanical garden. Ted was told by the gardener that there were 35 azaleas, 50 irises and 85 roses in the garden. What is the number of gerberas growing in the garden?\n<image1>", "hint": "", "options": {}, "choices": []}] | 110 | numeric | 3 | arithmetic | |
4 | [{"role": "user", "question": "How many different digits can you find in this picture?\n<image1>", "hint": "", "options": {}, "choices": []}] | 6 | numeric | 1 | counting | |
40 | [{"role": "user", "question": "Which shape cannot be seen in every picture?\n<image1>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | D | mcq | 1 | combinatorial geometry | |
400 | [{"role": "user", "question": "The construction in the picture is built of cubes of the same size and weighs 189 grams. How many grams does one cube weigh?\n<image1>", "hint": "", "options": {}, "choices": []}] | 21 | numeric | 5 | solid geometry | |
401 | [{"role": "user", "question": "If the length of the side of a little square is 1, what is the area of the letter N?\n<image1>", "hint": "", "options": {}, "choices": []}] | 18 | numeric | 2 | combinatorial geometry | |
402 | [{"role": "user", "question": "I surrounded the wooden circle (see picture) using $a \\mathrm{~cm}$ of thread. After that I surrounded by thread the wooden square –– $b \\mathrm{~cm}$ of thread was enough for that. How much thread (in $\\mathrm{cm}$ ) would be enough to surround the three wooden circles without moving ... | E | mcq | 3 | metric geometry - length | |
403 | [{"role": "user", "question": "The picture on the right has been drawn on paper and cut out to make a house. Which of the houses does it make?\n<image1>\n<image2>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | A | mcq | 5 | descriptive geometry | |
404 | [{"role": "user", "question": "A bar-code is formed by 17 alternating black and white bars (the first and the last bars are black). The black bars are of two types: wide and narrow. The number of white bars is greater by 3 than the number of wide black bars. Then the number of narrow black bars is\n<image1>", "hint": "... | 4 | numeric | 2 | algebra | |
405 | [{"role": "user", "question": "In the picture below you can see a road from town $M$ to town $N$ (a solid line) and a detour (a dashed line) of segment $K L$, which is under repair. How many more kilometers does one have to travel from $M$ to $N$ using the detour?\n<image1>", "hint": "", "options": {}, "choices": []}] | 6 | numeric | 3 | metric geometry - length | |
406 | [{"role": "user", "question": "Which numbers are written in the area that belongs to the rectangle and to the circle but doesn't belong to the triangle?\n<image1>", "hint": "", "options": {"A": "5 and 11", "B": "1 and 10", "C": "13", "D": "3 and 9", "E": "6, 7, and 4"}, "choices": []}] | B | mcq | 2 | combinatorial geometry | |
407 | [{"role": "user", "question": "How many white squares must you paint grey so that the number of grey squares is exactly half that of the white squares?\n<image1>", "hint": "", "options": {}, "choices": []}] | 3 | numeric | 3 | arithmetic | |
408 | [{"role": "user", "question": "Which of the rectangles $\\mathbf{A}$ to $\\mathbf{E}$ can be covered by the pattern on the right-hand side in such a way that the result is a totally black rectangle?\n<image1>\n<image2>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | D | mcq | 5 | descriptive geometry | |
409 | [{"role": "user", "question": "In this picture there is what I saw on four different clocks at the same time. Only one of them had the right time. One was 20 minutes fast. Another 20 minutes slow. One had stopped some time ago.\n<image1>\nWhat was the right time?", "hint": "", "options": {"A": "4:45", "B": "5:05", "C":... | B | mcq | 2 | logic | |
41 | [{"role": "user", "question": "How many triangles can you find in the picture?\n<image1>", "hint": "", "options": {}, "choices": []}] | 5 | numeric | 1 | counting | |
410 | [{"role": "user", "question": "A cube (on the right) is colored in three colors so that each face has exactly one color and the opposite face has the same color. Which of the following developments is the development of this cube?\n<image1>\n<image2>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E"... | E | mcq | 5 | solid geometry | |
411 | [{"role": "user", "question": "This figure is made of squares. What is the side of the biggest square?\n<image1>", "hint": "", "options": {}, "choices": []}] | 64 | numeric | 3 | metric geometry - length | |
412 | [{"role": "user", "question": "There are five houses on Color Street: a blue, a red, a yellow, a pink, and a green one. The houses are numbered from 1 to 5 (see picture). The red house is the neighbor of the blue house only. The blue house stands between the green and red houses.\n<image1>\nWhich color is the house wit... | E | mcq | 2 | logic | |
413 | [{"role": "user", "question": "A large cube consists of 125 small black and white cubes, such that any two adjacent faces of the small cubes have different colors, the corner cubes being black. How many small black cubes are used?\n<image1>", "hint": "", "options": {}, "choices": []}] | 63 | numeric | 5 | solid geometry | |
414 | [{"role": "user", "question": "This is a multiplication table. Which two letters represent the same number?\n<image1>", "hint": "", "options": {"A": "$L$ and $M$", "B": "$P$ and $N$", "C": "$R$ and $S$", "D": "$K$ and $R$", "E": "$M$ and $T$"}, "choices": []}] | E | mcq | 2 | algebra | |
415 | [{"role": "user", "question": "A butterfly sat down on a correctly solved exercise. What number is the butterfly covering?\n<image1>", "hint": "", "options": {}, "choices": []}] | 500 | numeric | 3 | arithmetic | |
416 | [{"role": "user", "question": "At noon the minute hand of a clock is in the position shown on the left and after the quarter of an hour -- in the position shown on the right. Which position the minute hand will take after seventeen quarters from the noon?\n<image1>\n<image2>", "hint": "", "options": {"A": "A", "B": "B"... | A | mcq | 3 | arithmetic | |
417 | [{"role": "user", "question": "In the diagram every of the eight kangaroos can jump to any empty square. What is the least number of kangaroos that must jump so that each row and each column have exactly two kangaroos?\n<image1>", "hint": "", "options": {}, "choices": []}] | 1 | numeric | 2 | counting | |
418 | [{"role": "user", "question": "John has a chocolate tablet consisting of square pieces of $1 \\mathrm{~cm} \\times 1 \\mathrm{~cm}$. He has eaten already some pieces in a corner (see the picture). How many pieces John still have?\n<image1>", "hint": "", "options": {}, "choices": []}] | 60 | numeric | 2 | metric geometry - area | |
419 | [{"role": "user", "question": "A square piece of paper has been cut in three pieces. Two of them are in the picture on the right. What is the third one?\n<image1>\n<image2>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | B | mcq | 2 | combinatorial geometry | |
42 | [{"role": "user", "question": "Which part of the house is missing?\n<image1>\n<image2>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | E | mcq | 1 | combinatorial geometry | |
420 | [{"role": "user", "question": "A frame of a rectangular picture is made from planks of equal width. What is the width of these planks (in centimetres) if the outside perimeter of the frame is $8 \\mathrm{~cm}$ more than the inside perimeter?\n<image1>", "hint": "", "options": {}, "choices": []}] | 1 | numeric | 2 | algebra | |
421 | [{"role": "user", "question": "You can make only one rectangle with the perimeter consisting of 6 matches (see the picture). How many different rectangles with the perimeter consisting of 14 matches can you compose?\n<image1>", "hint": "", "options": {}, "choices": []}] | 3 | numeric | 3 | combinatorics |
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