id stringlengths 1 4 | media images listlengths 1 1 | messages stringlengths 137 1.63k |
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1089 | [{"role": "user", "question": "The diagram shows a five-pointed star. How big is the angle $A$?\n<image1>", "answer": "C", "hint": "", "options": {}, "choices": [], "level": 5, "subject": "metric geometry - angle"}] | |
109 | [{"role": "user", "question": "Numbers were written on the petals of two flowers, with a number on each petal. One of the petals is hidden. The sum of the numbers written on the back flower is twice the sum of the numbers written on the front flower. What is the number written on the hidden petal?\n<image1>", "answer":... | |
1090 | [{"role": "user", "question": "Three equally sized equilateral triangles are cut from the vertices of a large equilateral triangle of side length $6 \\mathrm{~cm}$. The three little triangles together have the same perimeter as the remaining grey hexagon. What is the side-length of one side of one small triangle?\n<ima... | |
1091 | [{"role": "user", "question": "The diagram shows the 7 positions $1,2,3,4,5,6,7$ of the bottom side of a die which is rolled around its edge in this order. Which two of these positions were taken up by the same face of the die?\n<image1>", "answer": "B", "hint": "", "options": {}, "choices": [], "level": 4, "subject": ... | |
1092 | [{"role": "user", "question": "In a square $A B C D M$ is the midpoint of $A B$. $M N$ is perpenticular to $A C$. Determine the ratio of the area of the grey triangle to the area of the square $A B C D$.\n<image1>", "answer": "D", "hint": "", "options": {}, "choices": [], "level": 3, "subject": "metric geometry - area"... | |
1093 | [{"role": "user", "question": "A piece of string is folded as shown in the diagram by folding it in the middle, then folding it in the middle again und finally folding it in the middle once more. Then this folded piece of string is cut so that several pieces emerge. Amongst the resulting pieces there are some with leng... | |
1094 | [{"role": "user", "question": "Three lines disect a big triangle into four triangles and three quadrilaterals. The sum of the perimeters of the three quadrialterals is $25 \\mathrm{~cm}$. The sum of the perimeters of the four triangles is $20 \\mathrm{~cm}$. The perimeter of the big triangle is $19 \\mathrm{~cm}$. How ... | |
1095 | [{"role": "user", "question": "Triangle $A B C$ is equilateral and has area 9. The dividing lines are parallel to the sides, and divide the sides into three equal lengths. What is the area of the grey shaded part of the triangle?\n<image1>", "answer": "6", "hint": "", "options": {}, "choices": [], "level": 4, "subject"... | |
1096 | [{"role": "user", "question": "Melanie has a square piece of paper with a $4 \\times 4$ grid drawn on it. She cuts along the gridlines and cuts several shapes out which all look either the same as the one pictured, or the same as its mirror image. How many squares are left over if she cuts out as many shapes as possibl... | |
1097 | [{"role": "user", "question": "Anne plays 'sink the ship' with a friend, on a $5 \\times 5$ grid. She has already drawn in a $1 \\times 1$ ship and a $2 \\times 2$ ship (as shown in the picture). She must also draw a (rectangular) $3 \\times 1$ ship. Ships may be neither directly nor diagonally adjacent to each other. ... | |
1098 | [{"role": "user", "question": "The five shapes pictured were cut out of paper. Four of them can be folded to form a cube. For which shape is this not possible.\n<image1>", "answer": "C", "hint": "", "options": {}, "choices": [], "level": 4, "subject": "descriptive geometry"}] | |
1099 | [{"role": "user", "question": "In the $8 \\times 6$ grid pictured, there are 24 squares that have not been cut by either of the two diagonals. Now we draw the two diagonals on a $10 \\times 6$ grid. How many squares in this grid will not be cut by either of the two diagonals?\n<image1>", "answer": "32", "hint": "", "op... | |
11 | [{"role": "user", "question": "Mike has built a construction, shown in the upper picture, from equal cubes. Lily has taken several cubes out of it, thus Mike's construction became such as we see in the lower picture. How many cubes has Lily taken?\n<image1>", "answer": "7", "hint": "", "options": {}, "choices": [], "le... | |
110 | [{"role": "user", "question": "Six figures were drawn, one on each side of a cube, as shown beside, in different positions. On the side that does not appear beside is this drawing:\n<image1>\nWhat is the figure on the face opposite to it?\n<image2>\n<image3>", "answer": "B", "hint": "", "options": {}, "choices": [], "l... | |
1100 | [{"role": "user", "question": "Johann stacked $1 \\times 1$ cubes on the squares of a $4 \\times 4$ grid. The diagram on the right shows the number of cubes that were stacked on top of each other above each square. What will Johann see if he looks from the back (hinten) at the tower?\n<image1>\n<image2>", "answer": "C"... | |
1101 | [{"role": "user", "question": "The sides of the rectangle $A B C D$ are parallel to the co-ordinate axes. The rectangle is positioned below the $x$-axis and to the right of the $y$-axis, as shown in the picture. The co-ordinates of the points $A, B, C, D$ are whole numbers. For each of the points we calculate the value... | |
1102 | [{"role": "user", "question": "On a sheet of paper a grid is drawn such that each of the squares has sides $2 \\mathrm{~cm}$ long. How big is the area of the grey shaded quadrilateral $A B C D$?\n<image1>", "answer": "B", "hint": "", "options": {}, "choices": [], "level": 4, "subject": "combinatorial geometry"}] | |
1103 | [{"role": "user", "question": "Each of the 4 vertices and 6 edges of a tetrahedron is labelled with one of the numbers $1,2,3,4,5,6,7,8,9$ and 11. (The number 10 is left out). Each number is only used once. The number on each edge is the sum of the numbers on the two vertices which are connected by that edge. The edge ... | |
1104 | [{"role": "user", "question": "Four cars drive into a roundabout at the same point in time, each one coming from a different direction (see diagram). No car drives all the way around the roundabout, and no two cars leave at the same exit. In how many different ways can the cars exit the roundabout?\n<image1>", "answer"... | |
1105 | [{"role": "user", "question": "How many quadrilaterals of any size are to be found in the diagram pictured.\n<image1>", "answer": "4", "hint": "", "options": {}, "choices": [], "level": 3, "subject": "counting"}] | |
1106 | [{"role": "user", "question": "The area of rectangle $A B C D$ in the diagram is $10. M$ and $N$ are the midpoints of the sides $A D$ and $B C$ respectively. How big is the area of the quadrilateral $M B N D$?\n<image1>", "answer": "5", "hint": "", "options": {}, "choices": [], "level": 3, "subject": "metric geometry -... | |
1107 | [{"role": "user", "question": "Wanda has lots of pages of square paper, whereby each page has an area of 4. She cuts each of the pages into right-angled triangles and squares (see the left hand diagram). She takes a few of these pieces and forms the shape in the right hand diagram. How big is the area of this shape?\n<... | |
1108 | [{"role": "user", "question": "George builds the sculpture shown from seven cubes each of edge length 1. How many more of these cubes must he add to the sculpture so that he builds a large cube of edge length 3?\n<image1>", "answer": "20", "hint": "", "options": {}, "choices": [], "level": 4, "subject": "solid geometry... | |
1109 | [{"role": "user", "question": "Gray and white pearls are threaded onto a string. Tony pulls pearls from the ends of the chain. After pulling off the fifth gray pearl he stops. At most, how many white pearls could he have pulled off?\n<image1>", "answer": "7", "hint": "", "options": {}, "choices": [], "level": 5, "subje... | |
111 | [{"role": "user", "question": "Maria wants to write whole numbers in the squares of the figure, so that the sum of the numbers in three consecutive squares is always 10. She has already written a number. What number should she write on the gray square?\n<image1>", "answer": "2", "hint": "", "options": {}, "choices": []... | |
1110 | [{"role": "user", "question": "Five circles each with an area of $1 \\mathrm{~cm}^{2}$ overlap each other to form the figure in the diagram. The sections where two circles overlap, each have an area of $\\frac{1}{8} \\mathrm{~cm}^{2}$. How big is the area, which is completely covered by the figure in the diagram?\n<ima... | |
1111 | [{"role": "user", "question": "5 congruent rectangles are positioned in a square with side length 24 as shown in the diagram. How big is the area of one of these rectangles?\n<image1>", "answer": "E", "hint": "", "options": {}, "choices": [], "level": 3, "subject": "metric geometry - area"}] | |
1112 | [{"role": "user", "question": "In the following figure, the heart and the arrow are arranged as pictured. At the same moment the heart and the arrow begin to move. The arrow moves around the figure 3 spaces clockwise and the heart 4 spaces anticlockwise and then they stop. This process repeats itself over and over agai... | |
1113 | [{"role": "user", "question": "In triangle $A B C$ (see sketch) $A D$ is the angle bisector of the angle at $A$ and $B H$ is the height from side $A C$. The obtuse angle between $B H$ and $A D$ is four times the size of angle $\\angle D A B$. How big is the angle $\\angle C A B$?\n<image1>", "answer": "C", "hint": "", ... | |
1114 | [{"role": "user", "question": "Andy fills a $3 \\times 3$ table with all the digits from 1 to 9 so that each cell only contains one digit. He has already put the digits 1, 2, 3 and 4 in the table as shown in the diagram. Two numbers are 'neighbouring' when the cells they are in share one side. After he had finished fil... | |
1115 | [{"role": "user", "question": "The quadrilateral $A B C D$ has right angles only in corners $A$ and $D$. The numbers in the diagram give the respective areas of the triangles in which they are located. How big is the area of $A B C D$?\n<image1>", "answer": "45", "hint": "", "options": {}, "choices": [], "level": 3, "s... | |
1116 | [{"role": "user", "question": "Four identical cubes (see diagram) were fitted together. If the resulting shape is viewed from the front you see a black circle (picture on the right). What will you see on the back of the shape?\n<image1>\n<image2>", "answer": "A", "hint": "", "options": {}, "choices": [], "level": 4, "s... | |
1117 | [{"role": "user", "question": "On a pond 16 lilly pads are arranged in a $4 \\times 4$ grid as can be seen in the diagram. A frog sits on a lilly pad in one of the corners of the grid (see picture). The frog jumps from one lilly pad to another horizontally or vertically. In doing so he always jumps over at least one li... | |
1118 | [{"role": "user", "question": "A $5 \\times 5$ square is covered with $1 \\times 1$ tiles. The design on each tile is made up of three dark triangles and one light triangle (see diagram). The triangles of neighbouring tiles always have the same colour where they join along an edge. The border of the large square is mad... | |
1119 | [{"role": "user", "question": "The word KANGAROO is written on the top of my umbrella. Which of the following pictures shows my umbrella?\n<image1>\n<image2>", "answer": "E", "hint": "", "options": {}, "choices": [], "level": 4, "subject": "descriptive geometry"}] | |
112 | [{"role": "user", "question": "Turning a card around on the top side, we see the photo of the kangaroo. Instead, if we turn the card around on the right side, what will appear?\n<image1>\n<image2>", "answer": "D", "hint": "", "options": {}, "choices": [], "level": 2, "subject": "transformation geometry"}] | |
1120 | [{"role": "user", "question": "The diagram shows the net of a cube whose faces are numbered. Sascha adds the numbers that are on opposite faces of the cube. Which three results does he get?\n<image1>", "answer": "A", "hint": "", "options": {}, "choices": [], "level": 4, "subject": "descriptive geometry"}] | |
1121 | [{"role": "user", "question": "The diagram shows the net of a three-sided prism. Which line of the diagram forms an edge of the prism together with line UV when the net is folded up?\n<image1>", "answer": "C", "hint": "", "options": {}, "choices": [], "level": 4, "subject": "descriptive geometry"}] | |
1122 | [{"role": "user", "question": "When simon the squirrel comes down from his tree onto the floor, he never moves further than $5 \\mathrm{~m}$ away from the trunk of his tree. Furthermore, he stays at least $5 \\mathrm{~m}$ away from the dog kennel. Which picture shows most accurately the area in which Simon can be found... | |
1123 | [{"role": "user", "question": "One corner of a square piece of paper is folded into the middle of the square That way an irregular pentagon is created. The numerical values of the areas of the Pentagon and the square are consecutive whole numbers. What is the area of the square?\n<image1>", "answer": "8", "hint": "", "... | |
1124 | [{"role": "user", "question": "The diagram consists of three squares each one of side length 1. The midpoint of the topmost square is exactly above the common side of the two other squares. What is the area of the section coloured grey?\n<image1>", "answer": "1", "hint": "", "options": {}, "choices": [], "level": 4, "s... | |
1125 | [{"role": "user", "question": "A bush has 10 twigs. Each twig has exactly 5 leaves or exactly 2 leaves and a flower. Which of the following numbers could be the total number of leaves on the bush?\n<image1>", "answer": "E", "hint": "", "options": {}, "choices": [], "level": 4, "subject": "algebra"}] | |
1126 | [{"role": "user", "question": "Each side of each triangle in the diagram is painted either blue, green or red. Four of the sides are already painted. Which colour can the line marked \"x\" have, if each triangle must have all sides in different colours?\n<image1>", "answer": "A", "hint": "", "options": {}, "choices": [... | |
1127 | [{"role": "user", "question": "A square with area 30 is split into two by its diagonal and then Split into triangles as shown in the diagram. Some of the areas of the triangles are given in the diagram. Which of the line segments $a, b, c, d, e$ of the diagonal is the longest?\n<image1>", "answer": "D", "hint": "", "op... | |
1128 | [{"role": "user", "question": "Riki wants to write one number in each of the seven sections of the diagram pictured. Two zones are adjacent if they share a part of their outline. The number in each zone should be the sum of all numbers of its adjacent zones. Riki has already placed numbers in two zones. Which number do... | |
1129 | [{"role": "user", "question": "Florian has seven pieces of wire of lengths $1 \\mathrm{~cm}, 2 \\mathrm{~cm}, 3 \\mathrm{~cm}, 4 \\mathrm{~cm}, 5 \\mathrm{~cm}, 6 \\mathrm{~cm}$ and $7 \\mathrm{~cm}$. He uses some of those pieces to form a wire model of a cube with side length 1. He does not want any overlapping wire p... | |
113 | [{"role": "user", "question": "Tom has these nine cards:\n<image1>\nHe places these cards on the board next to each other so that each horizontal line and each vertical line has three cards with the three different shapes and the three different amounts of drawings. He has already placed three cards, as shown in the pi... | |
1130 | [{"role": "user", "question": "In the trapezium $P Q R S$ the sides $P Q$ and $S R$ are parallel. Also $\\angle \\mathrm{RSP}=120^{\\circ}$ and $\\overline{R S}=\\overline{S P}=\\frac{1}{3} \\overline{P Q}$. What is the size of angle $\\angle \\mathrm{PQR}$ ?\n<image1>", "answer": "D", "hint": "", "options": {}, "choic... | |
1131 | [{"role": "user", "question": "Which of the road signs has the most axes of symmetry?\n<image1>", "answer": "A", "hint": "", "options": {}, "choices": [], "level": 3, "subject": "transformation geometry"}] | |
1132 | [{"role": "user", "question": "What is the sum of the two marked angles?\n<image1>", "answer": "C", "hint": "", "options": {}, "choices": [], "level": 5, "subject": "metric geometry - angle"}] | |
1133 | [{"role": "user", "question": "A card has a diagram printed on one side and the other side is plain white. The card is first flipped over downwards and then to the right (see diagram). Which picture is obtained?\n<image1>\n<image2>", "answer": "B", "hint": "", "options": {}, "choices": [], "level": 3, "subject": "trans... | |
1134 | [{"role": "user", "question": "In the rectangle $A B C D$ the side $A D$ is $10 \\mathrm{~cm}$ long. $M$ and $N$ are the midpoints of the sides $A B$ and $C D$ respectively. How big is the grey area?\n<image1>", "answer": "C", "hint": "", "options": {}, "choices": [], "level": 3, "subject": "metric geometry - area"}] | |
1135 | [{"role": "user", "question": "During a cycle race starting at $D$ and finishing at $B$ every connecting road (between the towns $A, B, C$ and $D$ ) that is shown in the diagram will be ridden along exactly once. How many possible routes are there for the race?\n<image1>", "answer": "6", "hint": "", "options": {}, "cho... | |
1136 | [{"role": "user", "question": "Within the square $A B C D$ there are four identical rectangles (see diagram). The perimeter of each rectangle is $16 \\mathrm{~cm}$. What is the perimeter of this\nsquare?\n<image1>square?", "answer": "E", "hint": "", "options": {}, "choices": [], "level": 2, "subject": "metric geometry ... | |
1137 | [{"role": "user", "question": "Anne has glued together some cubes and has obtained the solid shown on the right. She turns it around to check it out from different sides. Which view can she not obtain?\n<image1>\n<image2>", "answer": "A", "hint": "", "options": {}, "choices": [], "level": 4, "subject": "solid geometry"... | |
1138 | [{"role": "user", "question": "A $3 \\mathrm{~cm}$ wide strip of paper is dark on one side and light on the other. The folded strip of paper lies exactly within a rectangle with length $27 \\mathrm{~cm}$ and width $9 \\mathrm{~cm}$ (see diagram). How long is the strip of paper?\n<image1>", "answer": "D", "hint": "", "o... | |
1139 | [{"role": "user", "question": "Seven identical dice (each with 1, 2, 3, 4, 5 and 6 points on their faces) are glued together to form the solid shown. Faces that are glued together each have the same number of points. How many points can be seen on the surface of the solid?\n<image1>", "answer": "105", "hint": "", "opti... | |
114 | [{"role": "user", "question": "Two equal trains, each with 31 numbered wagons, travel in opposite directions. When the wagon number 7 of a train is side by side with the wagon number 12 of the other train, which wagon is side by side with the wagon number 11 ?\n<image1>", "answer": "8", "hint": "", "options": {}, "choi... | |
1140 | [{"role": "user", "question": "In a square with area 36 there are grey parts as shown in the diagram. The sum of the areas of all grey parts is 27. How long are the distances $a, b, c$ and $d$ together?\n<image1>", "answer": "9", "hint": "", "options": {}, "choices": [], "level": 2, "subject": "metric geometry - length... | |
1141 | [{"role": "user", "question": "A big cube is made up of 64 small cubes. Exactly one of these cubes is grey (see diagram). Two cubes are neighbours if they share a common face. On day one the grey cube colours all its neighbouring cubes grey. On day two all grey cubes again colour all their neighbouring cubes grey. How ... | |
1142 | [{"role": "user", "question": "The diagram shows a pentagon and indicates the length of each side. Five circles are drawn with centres A, B, C, D and E. On each side of the pentagon the two circles that are drawn around the ends of that side touch each other. Which point is the centre of the biggest circle?\n<image1>",... | |
1143 | [{"role": "user", "question": "Susi writes a different positive whole number on each of the 14 cubes of the pyramid (see diagram). The sum of the numbers, which she writes on the nine cubes that lie on the bottom, is 50. The number on every remaining cube is equal to the sum of the numbers of the four cubes that are di... | |
1144 | [{"role": "user", "question": "A cube of side length 3 consists of 15 black and 12 white unit cubes. In the diagram five of the six faces of the big cube can be seen. Which of the regions shown below is the 6th face of the big cube?\n<image1>\n<image2>", "answer": "A", "hint": "", "options": {}, "choices": [], "level":... | |
1145 | [{"role": "user", "question": "The diagram shows an isosceles triangle, where the height is marked and its area is split up into equally wide white and grey stripes. Which fraction of the area of the triangle is white?\n<image1>", "answer": "A", "hint": "", "options": {}, "choices": [], "level": 3, "subject": "metric g... | |
1146 | [{"role": "user", "question": "The diagram shows two rectangles whose sides are parallel to each other. By how much is the perimeter of the bigger rectangle greater than the perimeter of the smaller rectangle?\n<image1>", "answer": "E", "hint": "", "options": {}, "choices": [], "level": 2, "subject": "metric geometry -... | |
1147 | [{"role": "user", "question": "Paul folds a piece of paper, then punches a hole into the paper and unfolds it again. The unfolded paper then looks like the picture on the right. Along which dotted line can Paul have folded the paper beforehand?\n<image1>\n<image2>", "answer": "D", "hint": "", "options": {}, "choices": ... | |
1148 | [{"role": "user", "question": "Petra crafts a piece of jewellery out of two black and two white hearts. The hearts have areas of $1 \\mathrm{~cm}^{2}, 4 \\mathrm{~cm}^{2}, 9 \\mathrm{~cm}^{2}$ and $16 \\mathrm{~cm}^{2}$ respectively. She places the hearts on top of each other as shown in the diagram and glues them toge... | |
1149 | [{"role": "user", "question": "Ant Annie starts at the left end of the stick and crawls $\\frac{2}{3}$ of the length of the stick. Ladybird Bob starts at the right end of the stick und crawls $\\frac{3}{4}$ of the length of the stick. Which fraction of the length of the stick are they then apart from each other?\n<imag... | |
115 | [{"role": "user", "question": "Six different numbers, chosen from integers 1 to 9 , are written on the faces of a cube, one number per face. The sum of the numbers on each pair of opposite faces is always the same. Which of the following numbers could have been written on the opposite side with the number 8 ?\n<image1>... | |
1150 | [{"role": "user", "question": "The black and the dashed line together form seven equilateral triangles. The dashed line is $20 \\mathrm{~cm}$ long. How long is the black line?\n<image1>", "answer": "D", "hint": "", "options": {}, "choices": [], "level": 2, "subject": "metric geometry - length"}] | |
1151 | [{"role": "user", "question": "Ria wants to write a number into each box. She has already written two numbers. The sum of all five numbers should be 35, the sum of the first three numbers should be 22, the sum of the last three numbers should be 25. What is the product Ria gets, if she multiplies the two numbers in the... | |
1152 | [{"role": "user", "question": "Two $1 \\mathrm{~cm}$ long segments are marked on opposite sides of a square with side length 8 $\\mathrm{cm}$. The end points of the segments are connected with each other as shown in the diagram. How big is the area of the grey part?\n<image1>", "answer": "B", "hint": "", "options": {},... | |
1153 | [{"role": "user", "question": "Emily wants to insert nine numbers into the $3 \\times 3$ table so that the sum of the numbers in two adjacent cells (with a common side) is always the same. She has already written two numbers into the table. How big is the sum of all nine numbers?\n<image1>", "answer": "22", "hint": "",... | |
1154 | [{"role": "user", "question": "There are 10 kangaroos in a row, as seen in the picture. Two kangaroos, that are standing next to each other and can see each other are allowed to change places by hopping past each other. This is carried out until no more jumps are allowed. How often do two kangaroos swap places?\n<image... | |
1155 | [{"role": "user", "question": "The diagram shows Maria's square tablecloth to scale. All small light squares are equally big and their diagonals are parallel to the sides of the table cloth. Which part of the whole table cloth is black?\n<image1>", "answer": "D", "hint": "", "options": {}, "choices": [], "level": 2, "s... | |
1156 | [{"role": "user", "question": "Mike has 125 small, equally big cubes. He glues some of them together in such a way that one big cube with exactly nine tunnels is created (see diagram). The tunnels go all the way straight through the cube. How many of the 125 cubes is he not using?\n<image1>", "answer": "39", "hint": ""... | |
1157 | [{"role": "user", "question": "Sarah wants to write a positive whole number onto every tile in the number wall shown, so that every number is equal to the sum of the two numbers on the tiles that are directly below. What is the maximum number of odd numbers Sarah can write on the tiles?\n<image1>", "answer": "10", "hin... | |
1158 | [{"role": "user", "question": "The parallelogram has area 1. The two diagonals intersect each other at point M. Another point $P$ lies on the side DC. $E$ is the point of intersection of the segments $A P$ and $B D$, and $F$ is the point of intersection of the segments $B P$ and $A C$. What is the area of the quadrilat... | |
1159 | [{"role": "user", "question": "If the letters of the Word MAMA are written underneath each other then the word has a vertical axis of symmetry. For which of these words does that also hold true?\n<image1>", "answer": "E", "hint": "", "options": {}, "choices": [], "level": 3, "subject": "transformation geometry"}] | |
116 | [{"role": "user", "question": "Rita numbered the circles of the figure from 1 to 8 , so that the sum of the three numbers on each of the four sides of the square equals 13 . What is the sum of the four numbers written on the colored circles?\n<image1>", "answer": "16", "hint": "", "options": {}, "choices": [], "level":... | |
1160 | [{"role": "user", "question": "The fence on the right has many holes. One morning the fence falls over and lies on the floor. Which of the following pictures shows the fallen down fence?\n<image1>\n<image2>", "answer": "C", "hint": "", "options": {}, "choices": [], "level": 4, "subject": "descriptive geometry"}] | |
1161 | [{"role": "user", "question": "Bernd produces steps for a staircase which are $15 \\mathrm{~cm}$ high and $15 \\mathrm{~cm}$ deep (see diagram). The staircase should reach from the ground floor to the first floor which is $3 \\mathrm{~m}$ higher. How many steps does Bernd have to produce?\n<image1>", "answer": "20", "h... | |
1162 | [{"role": "user", "question": "In a game of luck, A ball rolls downwards towards hammered nails and is diverted either to the right or the left by a nail immediately below it. One possible path is shown in the diagram. How many different ways are there for the ball to reach the second compartment from the left?\n<image... | |
1163 | [{"role": "user", "question": "A large rectangle is made up of 9 equally big rectangles. The longer side of each small rectangle is $10 \\mathrm{~cm}$ long. What is the perimeter of the large rectangle?\n<image1>", "answer": "C", "hint": "", "options": {}, "choices": [], "level": 4, "subject": "combinatorial geometry"}... | |
1164 | [{"role": "user", "question": "Two circles are inscribed into an $11 \\mathrm{~cm}$ long and $7 \\mathrm{~cm}$ wide rectangle so that they each touch three sides of the rectangle. How big is the distance between the centres of the two circles?\n<image1>", "answer": "D", "hint": "", "options": {}, "choices": [], "level"... | |
1165 | [{"role": "user", "question": "The square $A B C D$ has side length $3 \\mathrm{~cm}$. The points $M$ and $N$, which lie on the sides $A D$ and $A B$ respectively, are joined to the corner $C$. That way the square is split up into three parts with equal area. How long is the line segment DM?\n<image1>", "answer": "D", ... | |
1166 | [{"role": "user", "question": "Martina multiplies two, two-digit numbers and then paints over some of the digits. How big is the sum of the three digits that Martina has painted over?\n<image1>", "answer": "6", "hint": "", "options": {}, "choices": [], "level": 4, "subject": "algebra"}] | |
1167 | [{"role": "user", "question": "Valentin draws a zig-zag line inside a rectangle as shown in the diagram. For that he uses the angles $10^{\\circ}, 14^{\\circ}, 33^{\\circ}$ and $26^{\\circ}$. How big is angle $\\varphi$?\n<image1>", "answer": "A", "hint": "", "options": {}, "choices": [], "level": 5, "subject": "metric... | |
1168 | [{"role": "user", "question": "The diagram shows a rectangle and a straight line $x$, which is parallel to one of the sides of the rectangle. There are two points $A$ and $B$ on $x$ inside the rectangle. The sum of the areas of the two triangles shaded in grey is $10 \\mathrm{~cm}^{2}$. How big is the area of the recta... | |
1169 | [{"role": "user", "question": "Jakob writes one of the natural numbers 1 to 9 into each cell of the $3 \\times 3$-table. Then he works out the sum of the numbers in each row and in each column. Five of his results are 12, 13, 15, 16 and 17. What is the sixth sum?\n<image1>", "answer": "17", "hint": "", "options": {}, "... | |
117 | [{"role": "user", "question": "In the figure, an arrow pointing from one person to another means that the first person is shorter than the second. For example, person $B$ is shorter than person $A$. Which person is the tallest?\n<image1>", "answer": "C", "hint": "", "options": {}, "choices": [], "level": 3, "subject": ... | |
1170 | [{"role": "user", "question": "The diagram shows the net of a box consisting only of rectangles. How big is the volume of the box?\n<image1>", "answer": "C", "hint": "", "options": {}, "choices": [], "level": 4, "subject": "solid geometry"}] | |
1171 | [{"role": "user", "question": "Rita wants to write a number into every square of the diagram shown. Every number should be equal to the sum of the two numbers from the adjacent squares. Squares are adjacent if they share one edge. Two numbers are already given. Which number is she going to write into the square marked ... | |
1172 | [{"role": "user", "question": "Simon runs along the edge round a $50 \\mathrm{~m}$ long rectangular swimming pool, while at the same time Jan swims lengths in the pool. Simon runs three times as fast as Jan swims. While Jan swims 6 lengths, Simon manages 5 rounds around the pool. How wide is the swimming pool?\n<image1... | |
1173 | [{"role": "user", "question": "Lisas aviation club designs a flag with a flying \"dove\" on a $4 \\times 6$-grid. The area of the \"dove\" is $192 \\mathrm{~cm}^{2}$. The perimeter of the \"dove\" is made up of straight lines and circular arcs. What measurements does the flag have?\n<image1>", "answer": "D", "hint": ""... | |
1174 | [{"role": "user", "question": "The points $N, M$ and $L$ lie on the sides of an equilateral triangle $A B C$ so that $\\mathrm{NM} \\perp \\mathrm{BC}, \\mathrm{ML} \\perp \\mathrm{AB}$ and $\\mathrm{LN} \\perp \\mathrm{AC}$ holds true. The area of the triangle $\\mathrm{ABC}$ is $36 \\mathrm{~cm}^{2}$. What is the are... | |
1175 | [{"role": "user", "question": "In the isosceles triangle $A B C$ (with base $A C$ ) the points $K$ and $L$ are added on the sides $A B$ and $B C$ respectively so that $A K=K L=\\angle B$ and $K B=A C$. How big is the angle $\\angle A B C$?\n<image1>", "answer": "C", "hint": "", "options": {}, "choices": [], "level": 5,... | |
1176 | [{"role": "user", "question": "In a game of dominoes the tiles always have to be placed so that the touching halves of two adjacent domino tiles show the same number of dots. Paul has six domino tiles in front of him (see diagram).\n<image1>\nIn several steps Paul tries to arrange them in a correct order. In each step ... | |
1177 | [{"role": "user", "question": "Which cloud contains even numbers only?\n<image1>", "answer": "E", "hint": "", "options": {}, "choices": [], "level": 5, "subject": "arithmetic"}] | |
1178 | [{"role": "user", "question": "A $3 \\times 3 \\times 3$ cube is made up of small $1 \\times 1 \\times 1$ cubes. Then the middle cubes from front to back, from top to bottom and from right to left are removed (see diagram). How many $1 \\times 1 \\times 1$ - cubes remain?\n<image1>", "answer": "20", "hint": "", "option... |
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