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1179 | [{"role": "user", "question": "Three rings are connected to each other as shown. Which of the following pictures also shows three rings connected in the same way?\n<image1>\n<image2>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | D | mcq | 4 | descriptive geometry | |
118 | [{"role": "user", "question": "Maia the bee can only walk on colorful houses. How many ways can you color exactly three white houses with the same color so that Maia can walk from $A$ to $B$ ?\n<image1>", "hint": "", "options": {}, "choices": []}] | 16 | numeric | 1 | combinatorics | |
1180 | [{"role": "user", "question": "Four of the following five diagrams can be drawn without lifting the pencil and without going over a line twice. For one diagram this is not true. Which one is it?\n<image1>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | D | mcq | 3 | graph theory | |
1181 | [{"role": "user", "question": "A big square is divided up into smaller squares of different sizes as shown. Some of the smaller squares are shaded in grey. Which fraction of the big square is shaded in grey?\n<image1>", "hint": "", "options": {"A": "$\\frac{2}{3}$", "B": "$\\frac{2}{5}$", "C": "$\\frac{4}{7}$", "D": "$... | D | mcq | 3 | metric geometry - area | |
1182 | [{"role": "user", "question": "Three four-digit numbers are written onto three separate pieces of paper as shown. The sum of the three numbers is 10126. Three of the digits in the picture are hidden. Which are the hidden digits?\n<image1>", "hint": "", "options": {"A": "5,6 and 7", "B": "4,5 and 7", "C": "4,6 and 7", "... | A | mcq | 4 | algebra | |
1183 | [{"role": "user", "question": "The following information is known about triangle PSQ: $\\angle Q P S=20^{\\circ}$. The triangle PSQ has been split up into two smaller triangles by the line $Q R$ as shown. It is known that $P Q=P R=Q S$. How big is the angle RQS?\n<image1>", "hint": "", "options": {"A": "$50^{\\circ}$",... | B | mcq | 5 | metric geometry - angle | |
1184 | [{"role": "user", "question": "A $4 \\times 4$ square is made up of the two pieces shown. Which of the following $4 \\times 4$ squares cannot be made this way?\n<image1>\n<image2>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | E | mcq | 4 | combinatorial geometry | |
1185 | [{"role": "user", "question": "Kathi folds a square piece of paper twice and subsequently cuts it along the two lines as shown in the picture. The resulting pieces of paper are then unfolded if possible. How many of the pieces of paper are squares?\n<image1>", "hint": "", "options": {}, "choices": []}] | 5 | numeric | 3 | transformation geometry | |
1186 | [{"role": "user", "question": "Mia draws some congruent rectangles and one triangle. She then shades in grey those parts of the rectangles that lie outside the triangle (see diagram). How big is the resulting grey area?\n<image1>", "hint": "", "options": {"A": "$10 \\mathrm{~cm}^{2}$", "B": "$12 \\mathrm{~cm}^{2}$", "C... | B | mcq | 4 | combinatorial geometry | |
1187 | [{"role": "user", "question": "Anna has placed matches along the dotted lines to create a path. She has placed the first match as shown in the diagram. The path is in such a way that in the end it leads back to the left end of the first match. The numbers in the small squares state how many sides of the square she has ... | 16 | numeric | 4 | logic | |
1188 | [{"role": "user", "question": "n number of buttons are placed evenly around a circle. The buttons are labelled clockwise in order with the numbers 1 to $n$. The button with the number 7 is exactly opposite the button with the number 23. How big is $n$?\n<image1>", "hint": "", "options": {}, "choices": []}] | 32 | numeric | 4 | algebra | |
1189 | [{"role": "user", "question": "Natascha has some blue, red, yellow and green sticks of $1 \\mathrm{~cm}$ length. She wants to make a $3 \\times 3$ grid as shown in such a way that the four sides of each $1 \\times 1-$ square in the grid each are of a different colour. What is the minimum number of green sticks she can ... | 5 | numeric | 4 | combinatorial geometry | |
119 | [{"role": "user", "question": "A kangaroo laid out 3 sticks like this to make a shape. It is not allowed to break or to bend the sticks. Which shape could the kangaroo make?\n<image1>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | E | mcq | 1 | combinatorial geometry | |
1190 | [{"role": "user", "question": "An ant crawls along a closed line on the surface of a cube until it reaches its starting point. Which of the following nets of a cube belongs to the cube that the ant is crawling on?\n<image1>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | E | mcq | 3 | analytic geometry | |
1191 | [{"role": "user", "question": "Peter colours in each of the eight circles in one of the colours red, yellow or blue. Two circles that are directly connected by a line, are not allowed to be of the same colour. Which two circles does Peter definitely have to colour in the same colour?\n<image1>", "hint": "", "options": ... | A | mcq | 3 | graph theory | |
1192 | [{"role": "user", "question": "In square $A B C D, P, Q$ and $R$ are the midpoints of the edges $D A, B C$ and $C D$. Which fraction of the square $A B C D$ is shaded in the diagram?\n<image1>", "hint": "", "options": {"A": "$\\frac{3}{4}$", "B": "$\\frac{5}{8}$", "C": "$\\frac{1}{2}$", "D": "$\\frac{7}{16}$", "E": "$\... | E | mcq | 3 | metric geometry - area | |
1193 | [{"role": "user", "question": "One square was divided into four equal squares, containing other equal colored squares and equal colored triangles, as shown in the picture. What fraction of the original square does the colored part represent?\n<image1>", "hint": "", "options": {"A": "$\\frac{1}{3}$", "B": "$\\frac{1}{2}... | B | mcq | 4 | combinatorial geometry | |
1194 | [{"role": "user", "question": "The figure of side 1 is formed by six equal triangles, made with 12 sticks. How many matchsticks are needed to complete the figure of side 2, partially represented?\n<image1>", "hint": "", "options": {}, "choices": []}] | 36 | numeric | 4 | combinatorial geometry | |
1195 | [{"role": "user", "question": "Juca wrote a whole number greater than zero in each of the boxes on the $3 \\times 3$ board on the right, so that the sums of the numbers in each row and in each column are equal. The only thing Juca remembers is that there are no three numbers repeated. What number is written in the box ... | 4 | numeric | 4 | logic | |
1196 | [{"role": "user", "question": "In the figure, formed by a square and an equilateral triangle, the letters indicate the measurements of the angles. Which of the following equality is true?\n<image1>", "hint": "", "options": {"A": "$a=d$", "B": "$b+c=d$", "C": "$a+c=d+e$", "D": "$a+b=d+e$", "E": "$e+d=a$"}, "choices": []... | E | mcq | 5 | metric geometry - angle | |
1197 | [{"role": "user", "question": "As soon as he left his city towards Caecá, Charles saw the sign on the left. When he came back from Caecá, he saw the sign on the right. At that point, how far was it to get to his city?\n<image1>", "hint": "", "options": {"A": "$12 \\mathrm{~km}$", "B": "$21 \\mathrm{~km}$", "C": "$29 \\... | D | mcq | 4 | logic | |
1198 | [{"role": "user", "question": "Which of the pictures below shows what you will see if you look from above the piece represented on the right?\n<image1>\n<image2>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | C | mcq | 4 | descriptive geometry | |
1199 | [{"role": "user", "question": "The garden of Sonia's house is shaped like a 12-meter square and is divided into three lawns of the same area. The central lawn is shaped like a parallelogram, whose smaller diagonal is parallel to two sides of the square, as shown in the picture. What is the length of this diagonal, in m... | 8.0 | numeric | 2 | metric geometry - length | |
12 | [{"role": "user", "question": "Now it is 2008. What is the total sum of these digits?\n<image1>", "hint": "", "options": {}, "choices": []}] | 10 | numeric | 2 | arithmetic | |
120 | [{"role": "user", "question": "The picture shows 2 mushrooms. What is the difference between their heights?\n<image1>", "hint": "", "options": {}, "choices": []}] | 5 | numeric | 2 | arithmetic | |
1200 | [{"role": "user", "question": "Andrew bought 27 little cubes of the same color, each with three adjacent faces painted red and the other three of another color. He wants to use all these little cubes to build a bigger cube. What is the largest number of completely red faces that he can get for this cube?\n<image1>", "h... | 6 | numeric | 4 | solid geometry | |
1201 | [{"role": "user", "question": "A square is formed by four identical rectangles and a central square, as in the figure. The area of the square is $81 \\mathrm{~cm}^{2}$ and the square formed by the diagonals of these rectangles has an area equal to $64 \\mathrm{~cm}^{2}$. What is the area of the central square?\n<image1... | D | mcq | 5 | arithmetic | |
1202 | [{"role": "user", "question": "Irene made a \"city\" using identical wooden cubes. We have, beside, a view from above and a side view of this \"city\". We do not know which side of the \"city\" is being shown. What is the smallest amount of cubes Irene may have used to make its assembly?\n<image1>", "hint": "", "option... | 15 | numeric | 4 | descriptive geometry | |
1203 | [{"role": "user", "question": "Amelia has a paper strip with five equal cells containing different drawings, according to the figure. She folds the strip in such a way that the cells overlap in five layers. Which of the sequences of layers, from top to bottom, is not possible to obtain?\n<image1>\n<image2>", "hint": ""... | A | mcq | 3 | topology | |
1204 | [{"role": "user", "question": "Zilda took a square sheet of paper of side 1 and made two folds taking two consecutive sides of the sheet to a diagonal of it, as shown in the picture, obtaining a quadrilateral (highlighted outline). What is the area of this quadrilateral?\n<image1>", "hint": "", "options": {"A": "$\\fra... | B | mcq | 3 | transformation geometry | |
1205 | [{"role": "user", "question": "Cleuza assembled the $2 \\times 2 \\times 2$ block formed by equal balls beside, using one drop of glue at each contact point between two balls, in a total of 12 drops. She then glued a few more spheres until she completed a $4 \\times 3 \\times 2$ block. How many extra drops of glue did ... | 34 | numeric | 4 | solid geometry | |
1206 | [{"role": "user", "question": "Which of the following symbols for signs of the Zodiac has an axis of symmetry?\n<image1>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | A | mcq | 3 | transformation geometry | |
1207 | [{"role": "user", "question": "The figure shows three concentric circles with four lines passing through their common centre. What percentage of the figure is shaded?\n<image1>", "hint": "", "options": {"A": "$30 \\%$", "B": "$35 \\%$", "C": "$40 \\%$", "D": "$45 \\%$", "E": "$50 \\%$"}, "choices": []}] | E | mcq | 3 | metric geometry - area | |
1208 | [{"role": "user", "question": "When the 5 pieces <image1> are fitted together correctly, the result is a rectangle with a calculation written on it. What is the answer to this calculation?", "hint": "", "options": {}, "choices": []}] | -100 | numeric | 5 | arithmetic | |
1209 | [{"role": "user", "question": "Each of the five vases shown has the same height and each has a volume of 1 litre. Half a litre of water is poured into each vase. In which vase would the level of the water be the highest?\n<image1>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": [... | A | mcq | 4 | solid geometry | |
121 | [{"role": "user", "question": "Which of the paths shown in the pictures is the longest?\n<image1>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | A | mcq | 1 | counting | |
1210 | [{"role": "user", "question": "A cube $3 \\times 3 \\times 3$ is made from $1 \\times 1 \\times 1$ white, grey and black cubes, as shown in the first diagram. The other two diagrams show the white part and the black part of the cube. Which of the following diagrams shows the grey part?\n<image1>\n<image2>", "hint": "",... | E | mcq | 4 | descriptive geometry | |
1211 | [{"role": "user", "question": "A bike lock has four wheels numbered with the digits 0 to 9 in order. Each of the four wheels is rotated by $180^{\\circ}$ from the code shown in the first diagram to get the correct code. What is the correct code for the bike lock?\n<image1>\n<image2>", "hint": "", "options": {"A": "A", ... | B | mcq | 3 | transformation geometry | |
1212 | [{"role": "user", "question": "The area of the large square is $16 \\mathrm{~cm}^{2}$ and the area of each small square is $1 \\mathrm{~cm}^{2}$. What is the total area of the central flower in $\\mathrm{cm}^{2}$?\n<image1>", "hint": "", "options": {}, "choices": []}] | 4 | numeric | 3 | metric geometry - area | |
1213 | [{"role": "user", "question": "Costa is building a new fence in his garden. He uses 25 planks of wood, each of which are $30 \\mathrm{~cm}$ long. He arranges these planks so that there is the same slight overlap between any two adjacent planks. The total length of Costa's new fence is 6.9 metres. What is the length in ... | 2.5 | numeric | 5 | arithmetic | |
1214 | [{"role": "user", "question": "Five identical right-angled triangles can be arranged so that their larger acute angles touch to form the star shown in the diagram. It is also possible to form a different star by arranging more of these triangles so that their smaller acute angles touch. How many triangles are needed to... | 20 | numeric | 4 | combinatorial geometry | |
1215 | [{"role": "user", "question": "Five squares are positioned as shown. The small square indicated has area 1. What is the value of $h$?\n<image1>", "hint": "", "options": {"A": "$3 \\mathrm{~m}$", "B": "$3.5 \\mathrm{~m}$", "C": "$4 \\mathrm{~m}$", "D": "$4.2 \\mathrm{~m}$", "E": "$4.5 \\mathrm{~m}$"}, "choices": []}] | C | mcq | 2 | metric geometry - length | |
1216 | [{"role": "user", "question": "A rectangular strip of paper of dimensions $4 \\mathrm{~cm} \\times 13 \\mathrm{~cm}$ is folded as shown in the diagram. 2 rectangles are formed with areas $P$ and $Q$ where $P=2 Q$. What is the value of $x$?\n<image1>", "hint": "", "options": {"A": "$5 \\mathrm{~cm}$", "B": "$5.5 \\mathr... | C | mcq | 3 | transformation geometry | |
1217 | [{"role": "user", "question": "5 friends talk about their collected <image1>. Xenia says: \"I have an even number of pins\", Zach: \"Half of my pins are planets, Sue: \"I don't have any moons\", Paul: \"I have more moons than stars\" and Yvonne: \"I have more stars than planets\". Below are the collections of the 5 fri... | E | mcq | 4 | logic | |
1218 | [{"role": "user", "question": "A triangular pyramid is built with 20 cannon balls, as shown. Each cannon ball is labelled with one of $A, B, C, D$ or $E$. There are 4 cannon balls with each type of label. The picture shows the labels on the cannon balls on 3 of the faces of the pyramid. What is the label on the hidden ... | D | mcq | 4 | solid geometry | |
1219 | [{"role": "user", "question": "A $3 \\times 4 \\times 5$ cuboid consists of 60 identical small cubes. A termite eats its way along the diagonal from $P$ to $Q$. This diagonal does not intersect the edges of any small cube inside the cuboid. How many of the small cubes does it pass through on its journey?\n<image1>", "h... | 10 | numeric | 4 | solid geometry | |
122 | [{"role": "user", "question": "Four identical pieces of paper are placed as shown. Michael wants to punch a hole that goes through all four pieces. At which point should Michael punch the hole?\n<image1>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | D | mcq | 2 | descriptive geometry | |
1220 | [{"role": "user", "question": "In a tournament each of the 6 teams plays one match against every other team. In each round of matches, 3 take place simultaneously. A TV station has already decided which match it will broadcast for each round, as shown in the diagram. In which round will team D play against team F?\n<im... | 1 | numeric | 4 | logic | |
1221 | [{"role": "user", "question": "The diagram shows a quadrilateral divided into 4 smaller quadrilaterals with a common vertex $K$. The other labelled points divide the sides of the large quadrilateral into three equal parts. The numbers indicate the areas of the corresponding small quadrilaterals. What is the area of the... | 6 | numeric | 3 | metric geometry - area | |
1222 | [{"role": "user", "question": "Meike paddles around five buoys with her boat (see diagram). Which of the buoys does she paddle around in a clockwise direction?\n<image1>", "hint": "", "options": {"A": "2, 3 and 4", "B": "1, 2 and 3", "C": "1, 3 and 5", "D": "2, 4 and 5", "E": "2, 3 and 5"}, "choices": []}] | E | mcq | 3 | topology | |
1223 | [{"role": "user", "question": "The numbers 3, 4, 5, 6, 7 are written inside the five circles of the shape. The product of the numbers in the four outer circles is 360. Which number is in the inner circle?\n<image1>", "hint": "", "options": {}, "choices": []}] | 7 | numeric | 4 | algebra | |
1224 | [{"role": "user", "question": "Kengu likes to jump on the number line. He starts at 0 , then always starts with two big jumps and then three small jumps (see diagram). He keeps repeating this in the same way, over and over again. On which of the following numbers will he land in the course of his jumps?\n<image1>", "hi... | C | mcq | 4 | algebra | |
1225 | [{"role": "user", "question": "Sonja builds the cube shown, out of equally sized bricks. The shortest side of one brick is $4 \\mathrm{~cm}$ long. What dimensions in $\\mathrm{cm}$ does one brick have?\n<image1>", "hint": "", "options": {"A": "$4 \\times 6 \\times 12$", "B": "$4 \\times 6 \\times 16$", "C": "$4 \\times... | C | mcq | 4 | solid geometry | |
1226 | [{"role": "user", "question": "The black-white caterpillar shown, rolls up to go to sleep. Which diagram could show the rolled-up caterpillar?\n<image1>\n<image2>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | A | mcq | 3 | topology | |
1227 | [{"role": "user", "question": "Gerhard writes down the sum of the squares of two numbers. Unfortunately, some ink has run out (see diagram) and therefore we cannot read all the digits. What is the last digit of the first number?\n<image1>", "hint": "", "options": {}, "choices": []}] | 5 | numeric | 4 | algebra | |
1228 | [{"role": "user", "question": "There are five gaps in the following calculation. Adriana wants to write a \"+\" into four of the gaps and a \"−\" into one of the gaps so that the equation is correct. Where does she have to insert the \"-\"?\n<image1>", "hint": "", "options": {"A": "between 6 and 9", "B": "between 9 and... | D | mcq | 4 | algebra | |
1229 | [{"role": "user", "question": "There are 5 trees and 3 paths in a park as shown on the map. Another tree is planted so that there is an equal number of trees on both sides of each path. In\nwhich section of the park will the new tree be planted?\n<image1>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D"... | B | mcq | 4 | logic | |
123 | [{"role": "user", "question": "Ella puts on this t-shirt and stands in front of a mirror. Which of these images does she see in the mirror?\n<image1>\n<image2>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | A | mcq | 2 | descriptive geometry | |
1230 | [{"role": "user", "question": "The distance between two shelves in Monika's kitchen is $36 \\mathrm{~cm}$. She knows that a stack of 8 identical glasses is $42 \\mathrm{~cm}$ high and a stack of 2 such glasses is $18 \\mathrm{~cm}$ high. How many glasses has the biggest stack that will fit between two shelves?\n<image1... | 6 | numeric | 4 | algebra | |
1231 | [{"role": "user", "question": "On an ordinary die the numbers on opposite sides always add up to 7. Four such dice are glued together as shown. All numbers that can still be seen on the outside of the solid are added together. What is the minimum of that total?\n<image1>", "hint": "", "options": {}, "choices": []}] | 58 | numeric | 4 | algebra | |
1232 | [{"role": "user", "question": "Gardener Toni plants tulips <image1> and sunflowers <image2> in a square flowerbed with side length $12 \\mathrm{~m}$, as shown in the diagram. How big is the entire area where sunflowers are planted?\n<image3>", "hint": "", "options": {"A": "$36 \\mathrm{~m}^{2}$", "B": "$40 \\mathrm{~m}... | E | mcq | 3 | metric geometry - area | |
1233 | [{"role": "user", "question": "The big rectangle $A B C D$ is made up of 7 congruent smaller rectangles (see diagram). What is the ratio $\\frac{A B}{B C}$?\n<image1>", "hint": "", "options": {"A": "$\\frac{1}{2}$", "B": "$\\frac{4}{3}$", "C": "$\\frac{8}{5}$", "D": "$\\frac{12}{7}$", "E": "$\\frac{7}{3}$"}, "choices":... | D | mcq | 2 | metric geometry - length | |
1234 | [{"role": "user", "question": "Two identical bricks can be placed side by side in three different ways as shown in the diagrams. The surface areas of the resulting cuboids are 72, 96 and $102 \\mathrm{~cm}^{2}$. What is the surface area (in $\\mathrm{cm}^{2}$ ) of one brick?\n<image1>", "hint": "", "options": {}, "choi... | 54 | numeric | 4 | solid geometry | |
1235 | [{"role": "user", "question": "Jenny writes numbers into a $3 \\times 3$ table so that the sums of the four numbers in each $2 \\times 2$ area of the table are the same. The numbers in three of the cells in the corner can already be seen in the diagram. Which number does she write into the cell in the fourth corner?\n<... | 1 | numeric | 4 | algebra | |
1236 | [{"role": "user", "question": "A shape is made up of a triangle and a circle that partially overlap. The grey area is $45 \\%$ of the entire area of the shape. The white part of the triangle is $40 \\%$ of the total area of the shape. What percent of the area of the circle is the white part, outside the triangle?\n<ima... | B | mcq | 3 | metric geometry - area | |
1237 | [{"role": "user", "question": "The numbers 1 to 8 are written into the circles shown so that there is one number in each circle. Along each of the five straight arrows the three numbers in the circles are multiplied. Their product is written next to the tip of the arrow. How big is the sum of the numbers in the three c... | 17 | numeric | 4 | algebra | |
1238 | [{"role": "user", "question": "What is the minimum number of cells of a $5 \\times 5$ grid that have to be coloured in so that every possible $1 \\times 4$ rectangle and every $4 \\times 1$ rectangle respectively in the grid has at least one cell coloured in?\n<image1>", "hint": "", "options": {}, "choices": []}] | 6 | numeric | 4 | logic | |
1239 | [{"role": "user", "question": "The diagram shows a grid made of vertical and horizontal lines. Which part was cut from the grid? <image1>\n<image2>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | E | mcq | 4 | combinatorial geometry | |
124 | [{"role": "user", "question": "These children are standing in a line. Some are facing forwards and others are facing backwards. How many children are holding another child's hand with their right hand?\n<image1>", "hint": "", "options": {}, "choices": []}] | 6 | numeric | 1 | counting | |
1240 | [{"role": "user", "question": "Which of the following shapes cannot be cut into two trapeziums with one single straight line? <image1>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | A | mcq | 4 | combinatorial geometry | |
1241 | [{"role": "user", "question": "A dark disc with two holes is placed on top of a dial of a watch as shown. The dark disc is now rotated so that the number 8 can be seen through one of the holes. Which of the numbers could one see through the other hole now? <image1>", "hint": "", "options": {"A": "4 and 12", "B": "1 and... | A | mcq | 3 | transformation geometry | |
1242 | [{"role": "user", "question": "Kristina has a piece of see-through foil on which some points and lines are drawn. She folds the foil along the dotted line. <image1> What can she see now?", "hint": "", "options": {"A": "$2\\vdots6\\vdots9$", "B": "$2\\vdots6\\vdots6$", "C": "$5\\vdots6\\vdots6$", "D": "$2\\vdots8\\vdots... | C | mcq | 3 | transformation geometry | |
1243 | [{"role": "user", "question": "A $4\\times 6$ grid should be cut along the black lines into several identical shapes. No piece is to be left over. Into which of the following shapes is it not possible to cut this grid in this way? <image1> <image2>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": ... | D | mcq | 4 | combinatorial geometry | |
1244 | [{"role": "user", "question": "The diagram shows the starting position, the direction and the distance covered within 5 seconds by four bumper cars. Which two cars will first crash into each other? <image1>", "hint": "", "options": {"A": "A and B", "B": "A and C", "C": "A and D", "D": "B and C", "E": "C and D"}, "choic... | B | mcq | 3 | analytic geometry | |
1245 | [{"role": "user", "question": "Werner wants to label each side and each corner point of the rhombus shown with exactly one number. He wants the number on each side to be equal to the sum of the numbers on the corner points of that sides. Which number is he going to write in the place of the question mark? <image1>", "h... | 12 | numeric | 4 | algebra | |
1246 | [{"role": "user", "question": "Anna has five circular discs that are all of different sizes. She wants to build a tower using three discs where a smaller disc always has to lie on top of a bigger disc. How many ways are there for Anna to build the tower? <image1>", "hint": "", "options": {}, "choices": []}] | 10 | numeric | 2 | combinatorics | |
1247 | [{"role": "user", "question": "Evita wants to write the numbers from 1 to 8 with one number in each field. The sum of the numbers in each row should be equal. The sum of the numbers in the four columns should also be the same. She has already written in the numbers 3, 4 and 8 (see diagram). <image1> Which number does s... | 7 | numeric | 4 | logic | |
1248 | [{"role": "user", "question": "The diagram shows 5 equally big semicircles and the length of 5 distances. How big is the radius of one semicircle? <image1>", "hint": "", "options": {}, "choices": []}] | 18 | numeric | 2 | metric geometry - length | |
1249 | [{"role": "user", "question": "Some edges of a cube are coloured in red so that each sides of the cube has at least one red edge. What is the minimum number of red edges that the cube has? <image1>", "hint": "", "options": {}, "choices": []}] | 3 | numeric | 4 | solid geometry | |
125 | [{"role": "user", "question": "In the Kangaroo constellation, all stars have a number greater than 3 and their sum is 20 . Which is the Kangaroo constellation?\n<image1>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | B | mcq | 2 | arithmetic | |
1250 | [{"role": "user", "question": "The digits 0 to 9 can be formed using matchsticks (see diagram). How many different positive whole numbers can be formed this way with exactly 6 matchsticks? <image1>", "hint": "", "options": {}, "choices": []}] | 6 | numeric | 2 | combinatorics | |
1251 | [{"role": "user", "question": "Tom, John and Lily have each shot 6 arrows on a disc with three sections (see diagram). The number of points of a hit depends on the section that has been hit. Tom has 46 points and John has 34 points. How many points did Lily get? <image1>", "hint": "", "options": {}, "choices": []}] | 40 | numeric | 4 | algebra | |
1252 | [{"role": "user", "question": "Two rays starting in $S$ form a right angle. More rays starting in $S$ are drawn within the right angle so that each angle $10^{\\circ}, 20^{\\circ}, 30^{\\circ}, 40^{\\circ}, 50^{\\circ}, 60^{\\circ}, 70^{\\circ}$ and $80^{\\circ}$ is enclosed by two rays. What is the minimum number of r... | 3 | numeric | 4 | combinatorial geometry | |
1253 | [{"role": "user", "question": "The diagram shows a grey rectangle that lies within a bigger rectangle which sides it touches. Two corner points of the grey rectangle are the midpoints of the shorter sides of the bigger rectangle. The grey rectangle is made up of three squares that each have an area of $25 \\mathrm{~cm}... | 150 | numeric | 3 | metric geometry - area | |
1254 | [{"role": "user", "question": "The shown triangle $A B C$ is isosceles with $\\measuredangle A B C=40^{\\circ}$. The two angles indicated $\\measuredangle E A B$ and $\\measuredangle D C A$ are equally big. How big is the angle $\\measuredangle C F E$ ? <image1>", "hint": "", "options": {"A": "$55^{\\circ}$", "B": "$60... | D | mcq | 5 | metric geometry - angle | |
1255 | [{"role": "user", "question": "An ant walks along the sides of an equilateral triangle (see diagram). Its velocity is $5 \\mathrm{~cm} / \\mathrm{min}$ along the first side, $15 \\mathrm{~cm} / \\mathrm{min}$ along the second and $20 \\mathrm{~cm} / \\mathrm{min}$ along the third. With which average velocity in $\\math... | C | mcq | 4 | algebra | |
1256 | [{"role": "user", "question": "Elisabeth wants to write the numbers 1 to 9 in the fields of the diagram shown so that the product of the numbers of two fields next to each other is no greater than 15. Two fields are called „next to each other“ if they share a common edge. How many ways are there for Elisabeth to label ... | 16 | numeric | 2 | combinatorics | |
1257 | [{"role": "user", "question": "Several mice live in three houses. Last night every mouse left their house and moved directly to one of the other two houses. The diagram shows how many mice were in each house yesterday and today. How many mice used the path that is indicated with an arrow? <image1>", "hint": "", "option... | 11 | numeric | 4 | algebra | |
1258 | [{"role": "user", "question": "Bart wrote the number 1015 as a sum of numbers that are made up of only the digit 7 . In total he uses the digit 7, 10 times. Now he wants to the write the number 2023 as a sum of numbers that are made up of only the digit 7. He uses the digit 7, 19 times in total. How often does he have ... | 6 | numeric | 4 | algebra | |
1259 | [{"role": "user", "question": "A regular hexagon is split into four quadrilaterals and a smaller regular hexagon. The ratio $\\frac{\\text { Area of the dark sections }}{\\text { Area of the small hexagon }}=\\frac{4}{3}$. How big is the ratio $\\frac{\\text { Area of the small hexagon }}{\\text { Area of the big hexag... | A | mcq | 3 | metric geometry - area | |
126 | [{"role": "user", "question": "Edmund cut a ribbon as shown in the picture. How many pieces of the ribbon did he finish with?\n<image1>", "hint": "", "options": {}, "choices": []}] | 12 | numeric | 5 | topology | |
1260 | [{"role": "user", "question": "Jakob wrote six consecutive numbers on six little pieces of white paper, one number per piece of paper. He stuck those six pieces of paper on the front and back of three coins. Then he threw the coins three times. After the first throw the numbers 6, 7, 8 were on top (see diagram) which J... | 18 | numeric | 4 | algebra | |
1261 | [{"role": "user", "question": "$15 \\%$ of a round cake is cut as shown in the figure. How many degrees is the angle denoted by the question mark?\n<image1>", "hint": "", "options": {"A": "$30^{\\circ}$", "B": "$45^{\\circ}$", "C": "$54^{\\circ}$", "D": "$15^{\\circ}$", "E": "$20^{\\circ}$"}, "choices": []}] | C | mcq | 2 | metric geometry - angle | |
1262 | [{"role": "user", "question": "In the picture, three strips of the same horizontal width $a$ are marked 1,2,3. These strips connect the two parallel lines. Which strip has the biggest area?\n<image1>", "hint": "", "options": {"A": "All three strips have the same area", "B": "Strip 1", "C": "Strip 2", "D": "Strip 3", "E... | A | mcq | 4 | metric geometry - area | |
1263 | [{"role": "user", "question": "The area of the wooden square equals $a$. The area of each wooden circle equals $b$. Three circles are lined up as shown in the picture. If we tie together the three circles with a thread as short as possible, without moving them, what is the area inside the thread?\n<image1>", "hint": ""... | C | mcq | 4 | metric geometry - area | |
1264 | [{"role": "user", "question": "In this addition each of the letters $X, Y$ and $Z$ represents a different non-zero digit. The letter $X$ will then have to stand for\n<image1>", "hint": "", "options": {}, "choices": []}] | 8 | numeric | 3 | algebra | |
1265 | [{"role": "user", "question": "A rectangular parallelepiped was composed of 4 pieces, each consisting of 4 little cubes. Then one piece was removed (see picture) Which one?\n<image1>\n<image2>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | C | mcq | 3 | combinatorial geometry | |
1266 | [{"role": "user", "question": "In the picture there are four overlapping squares with sides 11, 9, 7 and 5 long. How much greater is the sum of the two grey areas than the sum of the two black areas?\n<image1>", "hint": "", "options": {}, "choices": []}] | 64 | numeric | 4 | metric geometry - area | |
1267 | [{"role": "user", "question": "The diagram shows four semicircles with radius 1. The centres of the semicircles are at the mid-points of the sides of a square. What is the radius of the circle which touches all four semicircles?\n<image1>", "hint": "", "options": {"A": "$\\sqrt{2}-1$", "B": "$\\frac{\\pi}{2}-1$", "C": ... | A | mcq | 4 | metric geometry - length | |
1268 | [{"role": "user", "question": "The graph of the function $f(x)$, defined for all real numbers, is formed by two half-lines and one segment, as illustrated in the picture. Clearly, -8 is a solution of the equation $f(f(x))=0$, because $f(f(-8))=f(-4)=0$. Find all the solutions of the equation $f(f(f(x)))=0$.\n<image1>",... | C | mcq | 5 | analytic geometry |
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