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1359 | [{"role": "user", "question": "One of the two sides of a rectangle has length $6 \\mathrm{~cm}$. In the rectangle circles are drawn next to each other in such a way that their centres form an equilateral triangle. What is the shortest distance between the two grey circles (in $\\mathrm{cm}$ )?\n<image1>", "hint": "", "... | C | mcq | 4 | metric geometry - length | |
136 | [{"role": "user", "question": "Stan has five toys: a ball, a set of blocks, a game, a puzzle and a car. He puts each toy on a different shelf of the bookcase. The ball is higher than the blocks and lower than the car. The game is directly above the ball. On which shelf can the puzzle not be placed?\n<image1>", "hint": ... | 3 | numeric | 3 | logic | |
1360 | [{"role": "user", "question": "The diagram shows a right-angled triangle with side lengths 5,12 and 13. What is the length of the radius of the inscribed semi-circle?\n<image1>", "hint": "", "options": {"A": "$7 / 3$", "B": "$10 / 3$", "C": "$12 / 3$", "D": "$13 / 3$", "E": "$17 / 3$"}, "choices": []}] | B | mcq | 4 | metric geometry - length | |
1361 | [{"role": "user", "question": "A number from 1 to 9 is to written into each of the 12 fields of the table so that the sum of each column is the same. Also the sum of each row must be the same. A few numbers have already been written in. Which number should be written in the grey square?\n<image1>", "hint": "", "options... | 4 | numeric | 5 | logic | |
1362 | [{"role": "user", "question": "A goldsmith has 12 double-links of chain. Out of these he wants to make a single closed chain with 24 links. What is the minimum number of links that he must open (and close again)?\n<image1>", "hint": "", "options": {}, "choices": []}] | 8 | numeric | 4 | arithmetic | |
1363 | [{"role": "user", "question": "A rectangle $A B C D$ with dimensions $16 \\mathrm{~cm}$ by $4 \\mathrm{~cm}$ was folded along the line MN so that corner C meets corner A. What is the area of the Pentagon ABNMD'?\n<image1>", "hint": "", "options": {"A": "$17 \\mathrm{~cm}^{2}$", "B": "$27 \\mathrm{~cm}^{2}$", "C": "$37 ... | D | mcq | 4 | transformation geometry | |
1364 | [{"role": "user", "question": "The shape pictured, is made out of two squares with side lengths $4 \\mathrm{~cm}$ and $5 \\mathrm{~cm}$ respectively, a triangle with area $8 \\mathrm{~cm}^{2}$ and the grey parallelogram. What is the area of the parallelogram?\n<image1>", "hint": "", "options": {"A": "$15 \\mathrm{~cm}^... | B | mcq | 4 | metric geometry - area | |
1365 | [{"role": "user", "question": "The natural numbers from 1 to 120 were written as shown into a table with 15 columns. In which column (counting from left) is the sum of the numbers the largest?\n<image1>", "hint": "", "options": {}, "choices": []}] | 5 | numeric | 3 | algebra | |
1366 | [{"role": "user", "question": "Maria has six equally big square pieces of plain paper. On each piece of paper she draws one of the figures shown below. How many of these figures have the same perimeter as the plain piece of paper itself?\n<image1>", "hint": "", "options": {}, "choices": []}] | 4 | numeric | 4 | metric geometry - length | |
1367 | [{"role": "user", "question": "Mrs. Maisl buys four pieces of corn-on-the-cob for each of the four members of her family and get the discount offered. How much does she end up paying?\n<image1>", "hint": "", "options": {"A": "$0.80 €$", "B": "$1.20 €$", "C": "$2.80 €$", "D": "$3.20 €$", "E": "$80 €$"}, "choices": []}] | C | mcq | 4 | arithmetic | |
1368 | [{"role": "user", "question": "On a square grid made up of unit squares, six points are marked as shown on the right. Three of which form a triangle with the least area. How big is this smallest area?\n<image1>", "hint": "", "options": {"A": "$1 / 2$", "B": "$1 / 3$", "C": "$1 / 4$", "D": "1", "E": "2"}, "choices": []}... | A | mcq | 3 | combinatorial geometry | |
1369 | [{"role": "user", "question": "A cube is coloured on the outside as if it was made up of four white and four black cubes where no cubes of the same colour are next to each other (see picture). Which of the following figures represents a possible net of the coloured cube?\n<image1>\n<image2>", "hint": "", "options": {"A... | E | mcq | 3 | descriptive geometry | |
137 | [{"role": "user", "question": "In which box are the most triangles?\n<image1>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | B | mcq | 1 | counting | |
1370 | [{"role": "user", "question": "In a drawing we can see a three quarter circle with centre M and an indicated orientation arrow. This three-quarter circle is first turned $90^{\\circ}$ anti-clockwise about M and then reflected in the x - axis. Which is the resulting picture?\n<image1>\n<image2>", "hint": "", "options": ... | D | mcq | 5 | analytic geometry | |
1371 | [{"role": "user", "question": "Triangle RZT is generated by rotating the equilateral triangle AZC about point Z. Angle $\\beta=\\angle \\mathrm{CZR}=70^{\\circ}$. Determine angle $\\alpha=\\angle \\mathrm{CAR}$.\n<image1>", "hint": "", "options": {"A": "$20^{\\circ}$", "B": "$25^{\\circ}$", "C": "$30^{\\circ}$", "D": "... | D | mcq | 2 | metric geometry - angle | |
1372 | [{"role": "user", "question": "The figure on the right is made up of six unit squares. Its perimeter is $14 \\mathrm{~cm}$. Squares will be added to this figure in the same way until it is made up of 2013 unit squares (zigzag: alternating bottom right and top right). How big is the perimeter of the newly created figure... | 4028 | numeric | 4 | arithmetic | |
1373 | [{"role": "user", "question": "A and B are opposite vertices of a regular six-side shape, the points $C$ and $D$ are the midpoints of two opposite sides. The area of the regular six-sided shape is 60. Determine the product of the lengths of the lines $A B$ and $C D$!\n<image1>", "hint": "", "options": {}, "choices": []... | 80 | numeric | 4 | arithmetic | |
1374 | [{"role": "user", "question": "The sides of the rectangle $A B C D$ are parallel to the co-ordinate axis. The rectangle lies below the $\\mathrm{x}$-axis and to the right of the $\\mathrm{y}$-axis, as shown in the diagram. For each of the points A, B, C, D the quotient (y-coordinate):(x-coordinate) is calculated. For w... | D | mcq | 5 | analytic geometry | |
1375 | [{"role": "user", "question": "Tarzan wanted to draw a rhombus made up of two equilateral triangles. He drew the line segments inaccurately. When Jane checked the measurements of the four angles shown, she sees that they are not equally big (see diagram). Which of the five line segments in this diagram is the longest?\... | A | mcq | 4 | metric geometry - length | |
1376 | [{"role": "user", "question": "How many different ways are there in the diagram shown, to get from point $A$ to point $B$ if you are only allowed to move in the directions indicated?\n<image1>", "hint": "", "options": {}, "choices": []}] | 12 | numeric | 4 | combinatorics | |
1377 | [{"role": "user", "question": "$a, b$ and $c$ show the lengths of the different of pieces of wire pictured. Which of the following inequalities is correct?\n<image1>", "hint": "", "options": {"A": "$a<b<c$", "B": "$a<c<b$", "C": "$b<a<c$", "D": "$b<c<a$", "E": "$c<b<a$"}, "choices": []}] | E | mcq | 3 | combinatorial geometry | |
1378 | [{"role": "user", "question": "The side lengths of the large regular hexagon are twice the length of those of the small regular hexagon. What is the area of the large hexagon if the small hexagon has an area of $4 \\mathrm{~cm}^{2}$?\n<image1>", "hint": "", "options": {"A": "$16 \\mathrm{~cm}^{2}$", "B": "$14 \\mathrm{... | A | mcq | 4 | metric geometry - area | |
1379 | [{"role": "user", "question": "The circumference of the large wheel measures $4.2 \\mathrm{~m}$, and that of the small wheel $0.9 \\mathrm{~m}$. To begin with the valves on both wheels are at the lowest point, and then the bicycle moves to the left. After a few metres both valves are again at the lowest point at the sa... | C | mcq | 4 | transformation geometry | |
138 | [{"role": "user", "question": "A sandwich and a juice cost 12 Euros together. A sandwich and two juices cost 14 Euros together. How many Euros does one juice cost?\n<image1>", "hint": "", "options": {}, "choices": []}] | 2 | numeric | 1 | algebra | |
1380 | [{"role": "user", "question": "Paul hangs rectangular pictures on a wall. For each picture he hammers a nail into the wall $2.5 \\mathrm{~m}$ above the floor. He ties a $2 \\mathrm{~m}$ long string to the upper corners of each picture (see diagram). which picture size (width in $\\mathrm{cm} \\times$ height in $\\mathr... | C | mcq | 4 | metric geometry - length | |
1381 | [{"role": "user", "question": "The shaded part of the regular octagon has an area of $3 \\mathrm{~cm}^{2}$. How big is the area of the octagon?\n<image1>", "hint": "", "options": {"A": "$8+4 \\sqrt{2} \\mathrm{~cm}^{2}$", "B": "$9 \\mathrm{~cm}^{2}$", "C": "$8 \\sqrt{2} \\mathrm{~cm}^{2}$", "D": "$12 \\mathrm{~cm}^{2}$... | D | mcq | 4 | metric geometry - area | |
1382 | [{"role": "user", "question": "If you add the numbers on opposite faces of this special die, you will get the same total three times. The numbers on the hidden faces of the die are prime numbers. Which number is on the face opposite to 14?\n<image1>", "hint": "", "options": {}, "choices": []}] | 23 | numeric | 5 | logic | |
1383 | [{"role": "user", "question": "In the diagram Karl wants to add lines joining two of the marked points at a time, so that each of the seven marked points is joined to the same number of other marked points. What is the minimum number of lines he must draw?\n<image1>", "hint": "", "options": {}, "choices": []}] | 9 | numeric | 4 | graph theory | |
1384 | [{"role": "user", "question": "The diagram shows two different views of the same cube. The cube is made from 27 small cubes, which are either white or black. At most how many black cubes are there?\n<image1>", "hint": "", "options": {}, "choices": []}] | 9 | numeric | 2 | solid geometry | |
1385 | [{"role": "user", "question": "$P T$ is the tangent to a circle $O$, and $P B$ is the angle bisector of the angle TPA (see diagram). How big is the angle TBP?\n<image1>", "hint": "", "options": {"A": "$30^{\\circ}$", "B": "$45^{\\circ}$", "C": "$50^{\\circ}$", "D": "$75^{\\circ}$", "E": "It depends on the location of p... | B | mcq | 2 | metric geometry - angle | |
1386 | [{"role": "user", "question": "In triangle $A B C, A B=6 \\mathrm{~cm}, A C=8 \\mathrm{~cm}$ and $B C=10 \\mathrm{~cm}$. $M$ is the midpoint of the side $B C$. $A M D E$ is a square and $M D$ intersects $A C$ at point $F$. What is the area of the quadrilateral $A F D E$ in $\\mathrm{cm}^{2}$?\n<image1>", "hint": "", "o... | B | mcq | 4 | metric geometry - area | |
1387 | [{"role": "user", "question": "The grey areas of the square with side length $a$ are bounded by a semi-circle and two quarter-circles respectively. What is their total area?\n<image1>", "hint": "", "options": {"A": "$\\frac{\\pi a^{2}}{8}$", "B": "$\\frac{a^{2}}{2}$", "C": "$\\frac{\\pi a^{2}}{2}$", "D": "$\\frac{a^{2}... | B | mcq | 4 | metric geometry - area | |
1388 | [{"role": "user", "question": "Mr. Hide wants to find a treasure that he buried years before. He can only remember that he buried the treasure at least $5 \\mathrm{~m}$ away from the hedge and no more than $5 \\mathrm{~m}$ away from the old pear tree. Which picture shows best the area where Mr. Hide has to look for the... | B | mcq | 4 | metric geometry - area | |
1389 | [{"role": "user", "question": "In the diagram one can see my decision-die in three different positions. What is the probability I get a \"YES\", when rolling this die once.\n<image1>", "hint": "", "options": {"A": "$\\frac{1}{3}$", "B": "$\\frac{1}{2}$", "C": "$\\frac{5}{9}$", "D": "$\\frac{2}{3}$", "E": "$\\frac{5}{6}... | B | mcq | 2 | solid geometry | |
139 | [{"role": "user", "question": "Anna cuts the picture of a mushroom in two halves.\n<image1>\nShe then arranges the two pieces together to form a new picture. What could this new picture look like?\n<image2>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | E | mcq | 1 | combinatorial geometry | |
1390 | [{"role": "user", "question": "The side lengths of each of the small squares in the diagram are 1. How long is the shortest path from \"Start\" to \"Ziel\", if you are only allowed to move along the sides and the diagonals of the squares?\n<image1>", "hint": "", "options": {"A": "$2 \\sqrt{5}$", "B": "$\\sqrt{10}+\\sqr... | C | mcq | 3 | combinatorial geometry | |
1391 | [{"role": "user", "question": "The square $A B C D$ has area 80. The points $E, F, G$ and $H$ are on the sides of the square and $\\mathrm{AE}=\\mathrm{BF}=\\mathrm{CG}=\\mathrm{DH}$. How big is the area of the grey part, if $\\mathrm{AE}=3 \\times \\mathrm{EB}$?\n<image1>", "hint": "", "options": {}, "choices": []}] | 25 | numeric | 4 | metric geometry - area | |
1392 | [{"role": "user", "question": "Four objects $a, b, c, d$ are placed on a double balance as shown. Then two of the objects are exchanged, which results in the change of position of the balance as shown. Which two objects were exchanged?\n<image1>", "hint": "", "options": {"A": "$a$ and $b$", "B": "$b$ and $d$", "C": "$b... | D | mcq | 3 | algebra | |
1393 | [{"role": "user", "question": "In the diagram we can see seven sections which are bordered by three circles. One number is written into each section. It is known that each number is equal to the sum of all the numbers in the adjacent zones. (Two zones are called adjacent if they have more than one corner point in commo... | 0 | numeric | 5 | logic | |
1394 | [{"role": "user", "question": "Lines parallel to the base $A C$ of triangle $A B C$ are drawn through $X$ and $Y$. In each case, the areas of the grey parts are equal in siz. The ratio $B X: X A=4: 1$ is known. What is the ratio $B Y: Y A$?\n<image1>", "hint": "", "options": {"A": "$1: 1$", "B": "$2: 1$", "C": "$3: 1$"... | D | mcq | 4 | metric geometry - length | |
1395 | [{"role": "user", "question": "A $3 \\times 3$ field is made up of 9 unit squares. In two of these squares, circles are inscribed as shown in the diagram. How big is the shortest distance between these circles?\n<image1>", "hint": "", "options": {"A": "$2 \\sqrt{2}-1$", "B": "$\\sqrt{2+1}$", "C": "$2 \\sqrt{2}$", "D": ... | A | mcq | 4 | metric geometry - length | |
1396 | [{"role": "user", "question": "What percentage of the area of the triangle is coloured in grey in the adjacent diagram?\n<image1>", "hint": "", "options": {"A": "$80 \\%$", "B": "$85 \\%$", "C": "$88 \\%$", "D": "$90 \\%$", "E": "It cannot be calculated."}, "choices": []}] | C | mcq | 4 | metric geometry - area | |
1397 | [{"role": "user", "question": "Jilly makes up a multiplication magic square using the numbers $1,2,4,5,10,20,25,50$ and 100. The products of the numbers in each row, column and diagonal should be equal. In the diagram it can be seen how she has started. Which number goes into the cell with the question mark?\n<image1>"... | 4 | numeric | 4 | arithmetic | |
1398 | [{"role": "user", "question": "Jack wants to keep six tubes each of diameter $2 \\mathrm{~cm}$ together using a rubber band. He chooses between the two possible variations shown. How are the lengths of the rubber bands related to each other?\n<image1>", "hint": "", "options": {"A": "In the left picture the band is $\\p... | E | mcq | 4 | metric geometry - length | |
1399 | [{"role": "user", "question": "Peter wants to colour in the cells of a $3 \\times 3$ square so that every row, every column and both diagonals each have three cells with three different colours. What is the smallest number of colours with which Peter can achieve this?\n<image1>", "hint": "", "options": {}, "choices": [... | 5 | numeric | 4 | combinatorics | |
14 | [{"role": "user", "question": "Mary has written all the numbers from 1 to 30 . How many times has she written digit 2?\n<image1>", "hint": "", "options": {}, "choices": []}] | 13 | numeric | 1 | counting | |
140 | [{"role": "user", "question": "In the four squares of a row there always have to be exactly two coins. In the four squares below each other there also always have to be exactly two coins.\n<image1>\nOn which square does one more coin have to be placed?", "hint": "", "options": {"A": "square $A$", "B": "square $B$", "C"... | D | mcq | 3 | logic | |
1400 | [{"role": "user", "question": "In the diagram we see a cube and four marked angles. How big is the sum of those angles?\n<image1>", "hint": "", "options": {"A": "$315^{\\circ}$", "B": "$330^{\\circ}$", "C": "$345^{\\circ}$", "D": "$360^{\\circ}$", "E": "$375^{\\circ}$"}, "choices": []}] | B | mcq | 2 | solid geometry | |
1401 | [{"role": "user", "question": "A creeping plant twists exactly 5 times around a post with circumference $15 \\mathrm{~cm}$ (as shown in the diagram) and thus reaches a height of $1 \\mathrm{~m}$. While the plant grows the height of the plant also grows with constant speed. How long is the creeping plant?\n<image1>", "h... | C | mcq | 2 | solid geometry | |
1402 | [{"role": "user", "question": "We consider a $5 \\times 5$ square that is split up into 25 fields. Initially all fields are white. In each move it is allowed to change the colour of two fields that are horizontally or vertically adjacent (i.e. white fields turn black and black ones turn white). What is the smallest num... | 12 | numeric | 4 | graph theory | |
1403 | [{"role": "user", "question": "Peter writes the word KANGAROO on a see-through piece of glass, as seen on the right. What can he see when he first flips over the glass onto its back along the right-hand side edge and then turns it about $180^{\\circ}$ while it is lying on the table?\n<image1>\n<image2>", "hint": "", "o... | E | mcq | 4 | transformation geometry | |
1404 | [{"role": "user", "question": "A wheel rolls along a zigzag curve as can be seen below. Which of the following pictures shows the curve that is described by the centre of the wheel?\n<image1>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | E | mcq | 4 | transformation geometry | |
1405 | [{"role": "user", "question": "A circle with radius 1 rolls along a straight line from point $K$ to point $L$, as shown, with $K L=11 \\pi$. In which position is the circle when it has arrived in $L$?\n<image1>\n<image2>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | E | mcq | 4 | transformation geometry | |
1406 | [{"role": "user", "question": "$A B C D$ is a trapezium with parallel sides $A B$ and $C D$. Let $A B=50$ and $C D=20$. Point $E$ lies on side $A B$ in such a way that the straight line $D E$ divides the trapezium into two shapes of equal area. How long is the straight line $A E$?\n<image1>", "hint": "", "options": {},... | 35 | numeric | 4 | metric geometry - length | |
1407 | [{"role": "user", "question": "In an equilateral triangle with area 1, we draw the six perpendicular lines from the midpoints of each side to the other two sides as seen in the diagram. How big is the area of the grey hexagon that has been created this way?\n<image1>", "hint": "", "options": {"A": "$\\frac{1}{3}$", "B"... | D | mcq | 4 | metric geometry - area | |
1408 | [{"role": "user", "question": "A belt system is made up of wheels $A, B$ and $C$, which rotate without sliding. $B$ rotates 4 times around, while $A$ turns 5 times around, and $B$ rotates 6 times around, while $C$ turns 7 times around. The circumference of $C$ is $30 \\mathrm{~cm}$. How big is the circumference of $A$?... | B | mcq | 4 | metric geometry - length | |
1409 | [{"role": "user", "question": "Jenny wants to write numbers into the cells of a $3 \\times 3$-table so that the sum of the numbers in each of the four $2 \\times 2$-squares are equally big. As it is shown in the diagram, she has already inserted three numbers. What number does she have to write into the cell in the fou... | 0 | numeric | 5 | logic | |
141 | [{"role": "user", "question": "A monkey has torn off a piece of Captain Jack's map.\n<image1>\nWhat does the piece the monkey has torn off look like?\n<image2>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | B | mcq | 1 | combinatorial geometry | |
1410 | [{"role": "user", "question": "In a convex quadrilateral $A B C D$ the diagonals are perpendicular to each other. The length of the edges are $A B=2017, B C=2018$ and $C D=2019$ (diagram not to scale). How long is side $A D$?\n<image1>", "hint": "", "options": {"A": "2016", "B": "2018", "C": "$\\sqrt{2020^{2}-4}$", "D"... | D | mcq | 4 | metric geometry - length | |
1411 | [{"role": "user", "question": "Paul 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 he can write on the tiles?\n<image1>", "hint": "", "options": {... | 14 | numeric | 4 | combinatorics | |
1412 | [{"role": "user", "question": "Three weights are randomly placed on each tray of a beam balance. The balance dips to the right hand side as shown on the picture. The masses of the weights are 101, 102, 103, 104, 105 and 106 grams. For how many percent of the possible distributions is the 106grams-weight on the right (h... | B | mcq | 4 | combinatorics | |
1413 | [{"role": "user", "question": "The points $A$ and $B$ lie on a circle with centre $M$. The point $P$ lies on the straight line through $A$ and $M. P B$ touches the circle in $B$. The lengths of the segments $P A$ and $M B$ are whole numbers, and $P B=P A+6$. How many possible values for $M B$ are there?\n<image1>", "hi... | 6 | numeric | 4 | metric geometry - length | |
1414 | [{"role": "user", "question": "The rings shown are partially interlinked. How long is the longest chain built this way which also contains the thick light ring?\n<image1>", "hint": "", "options": {}, "choices": []}] | 5 | numeric | 2 | topology | |
1415 | [{"role": "user", "question": "The distance between the top of the cat that is sitting on the table to the top of the cat that is sleeping on the floor is $150 \\mathrm{~cm}$. The distance from the top of the cat that is sleeping on the table to the top of the cat that is sitting on the floor is $110 \\mathrm{~cm}$. Ho... | C | mcq | 3 | algebra | |
1416 | [{"role": "user", "question": "In the three regular hexagons shown, $X, Y$ and $Z$ describe in this order the areas of the grey shaded parts. Which of the following statements is true?\n<image1>", "hint": "", "options": {"A": "$X=Y=Z$", "B": "$Y=Z \\neq X$", "C": "$Z=X \\neq Y$", "D": "$X=Y \\neq Z$", "E": "Each of the... | A | mcq | 4 | metric geometry - area | |
1417 | [{"role": "user", "question": "In the (correct) calculation shown, some of the digits were replaced by the letters P, Q, R and S. What is the value of $P+Q+R+S$?\n<image1>", "hint": "", "options": {}, "choices": []}] | 15 | numeric | 3 | algebra | |
1418 | [{"role": "user", "question": "In the diagram shown, you should follow the arrows to get from A to B. How many different ways are there that fulfill this condition?\n<image1>", "hint": "", "options": {}, "choices": []}] | 16 | numeric | 4 | combinatorics | |
1419 | [{"role": "user", "question": "Eight congruent semi-circles are drawn inside a square with side length 4. How big is the area of the white part?\n<image1>", "hint": "", "options": {}, "choices": []}] | 8 | numeric | 4 | metric geometry - area | |
142 | [{"role": "user", "question": "These five animals are made up from different shapes. There is one shape which is only used on one animal. On which animal is this shape used?\n<image1>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | D | mcq | 1 | combinatorial geometry | |
1420 | [{"role": "user", "question": "Two concentric circles with radii 1 and 9 form an annulus. $n$ circles without overlap are drawn inside this annulus, where every circle touches both circles of the annulus. (The diagram shows an example for $\\mathrm{n}=1$ and the other radii as given.) What is the biggest possible value... | 3 | numeric | 3 | combinatorial geometry | |
1421 | [{"role": "user", "question": "A number is to be written into every vertex of the 18 -sided shape so that it is equal to the sum of the two numbers from the adjacent vertices. Two of these numbers are given. Which number is written in vertex $A$?\n<image1>", "hint": "", "options": {}, "choices": []}] | 38 | numeric | 3 | algebra | |
1422 | [{"role": "user", "question": "Diana draws a rectangle made up of twelve squares onto a piece of squared paper. Some of the squares are coloured in black. She writes the number of adjacent black squares into every white square. The diagram shows an example of such a rectangle. Now she does the same with a rectangle mad... | 3025 | numeric | 5 | logic | |
1423 | [{"role": "user", "question": "Seven little dice were removed from a $3 \\times 3 \\times 3$ die, as can be seen in the diagram. The remaining (completely symmetrical) figure is cut along a plane through the centre and perpendicular to one of the four space diagonals. What does the cross-section look like?\n<image1>\n<... | A | mcq | 3 | descriptive geometry | |
1424 | [{"role": "user", "question": "Two chords $A B$ and $A C$ are drawn into a circle with diameter $\\mathrm{AD}. \\angle B A C=60^{\\circ}$, $\\overline{A B}=24 \\mathrm{~cm}$, $\\mathrm{E}$ lies on $\\mathrm{AC}$ so that $\\overline{E C}=3 \\mathrm{~cm}$, and $\\mathrm{BE}$ is perpendicular to $\\mathrm{AC}$. How long i... | D | mcq | 4 | metric geometry - length | |
1425 | [{"role": "user", "question": "A barber wants to write the word SHAVE on a board so that a customer who sees the word in the mirror can read the word normally. How does he have to write the word on the board?\n<image1>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | E | mcq | 4 | transformation geometry | |
1426 | [{"role": "user", "question": "Five identical measuring jugs are filled with water. Four of them contain exactly the same amount of water. Which measuring jug contains a different amount?\n<image1>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | B | mcq | 1 | statistics | |
1427 | [{"role": "user", "question": "Which of the following statements is definitely true for the angle marked in the diagram which is made up of nine squares?\n<image1>", "hint": "", "options": {"A": "$\\alpha=\\beta$", "B": "$2 \\alpha+\\beta=90^{\\circ}$", "C": "$\\alpha+\\beta=60^{\\circ}$", "D": "$2 \\beta+\\alpha=90^{\... | B | mcq | 2 | metric geometry - angle | |
1428 | [{"role": "user", "question": "Inside a unit square a certain area has been coloured in black. In which square is the black area biggest?\n<image1>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | A | mcq | 4 | metric geometry - area | |
1429 | [{"role": "user", "question": "Three five-digit numbers are written onto three separate pieces of paper as shown. Three of the digits in the picture are hidden. The sum of the three numbers is 57263. Which are the hidden digits?\n<image1>", "hint": "", "options": {"A": "0,2 and 2", "B": "1,2 and 9", "C": "2,4 and 9", "... | B | mcq | 3 | algebra | |
143 | [{"role": "user", "question": "There is an animal asleep in each of the five baskets. The koala and the fox sleep in baskets with the same pattern and the same shape. The kangaroo and the rabbit sleep in baskets with the same pattern.\n<image1>\nIn which basket does the mouse sleep?", "hint": "", "options": {"A": "Bask... | E | mcq | 3 | logic | |
1430 | [{"role": "user", "question": "The flag of Kanguria is a rectangle whose side lengths are in the ratio $3: 5$. The flag is split into four rectangles of equal area as shown. In which ratio are the side lengths of the white rectangle?\n<image1>", "hint": "", "options": {"A": "$1: 3$", "B": "$1: 4$", "C": "$2: 7$", "D": ... | E | mcq | 4 | metric geometry - length | |
1431 | [{"role": "user", "question": "A $3 \\times 2$ rectangle can be covered in two ways by two of the L-shaped figures as shown:\n<image1>\nIn how many ways can the diagram below be covered by these L-shaped figures?\n<image2>", "hint": "", "options": {}, "choices": []}] | 2 | numeric | 3 | combinatorial geometry | |
1432 | [{"role": "user", "question": "The diagram consists of three circles of equal radius $R$. The centre of those circles lie on a common straight line where the middle circle goes through the centres of the other two circles (see diagram). How big is the perimeter of the figure?\n<image1>", "hint": "", "options": {"A": "$... | A | mcq | 4 | metric geometry - length | |
1433 | [{"role": "user", "question": "The diagram shows the net of an octahedron. Which edge meets the edge labelled with $\\mathrm{x}$ if the net is folded up to form an octahedron?\n<image1>", "hint": "", "options": {}, "choices": []}] | 5 | numeric | 2 | solid geometry | |
1434 | [{"role": "user", "question": "Two vertices of a square lie on a semi-circle as shown, while the other two lie on its diameter. The radius of the circle is $1 \\mathrm{~cm}$. How big is the area of the square?\n<image1>", "hint": "", "options": {"A": "$\\frac{4}{5} \\mathrm{~cm}^{2}$", "B": "$\\frac{\\pi}{4} \\mathrm{~... | A | mcq | 4 | metric geometry - area | |
1435 | [{"role": "user", "question": "A graph consists of 16 points and several connecting lines as shown in the diagram. An ant is at point $A$. With every move the ant can move from the point where it currently is, along one of the connecting lines, to an adjacent point. At which of the points $P, Q, R, S$ and $T$ can the a... | C | mcq | 3 | algebra | |
1436 | [{"role": "user", "question": "When Cosme correctly wears his new shirt, as shown on the left figure, the horizontal stripes form seven closed arches around his body. This morning he buttoned his shirt in the wrong way, as shown on the right. How many open arches were there around Cosme's body this morning?\n<image1>",... | 1 | numeric | 4 | counting | |
1437 | [{"role": "user", "question": "In the addition beside, different letters represent different numbers and equal letters represent equal numbers. The resulting sum is a number of four digits, B being different from zero. What is the sum of the numbers of this number?\n<image1>", "hint": "", "options": {"A": "AA", "B": "B... | B | mcq | 3 | algebra | |
1438 | [{"role": "user", "question": "There are several figures that can be formed by nine squares of $1 \\mathrm{~cm}$ side by side (see an example beside) and one of them has the biggest perimeter. What is this perimeter?\n<image1>", "hint": "", "options": {"A": "$12 \\mathrm{~cm}$", "B": "$14 \\mathrm{~cm}$", "C": "$16 \\m... | E | mcq | 3 | combinatorial geometry | |
1439 | [{"role": "user", "question": "Four points were marked on a grid of $1 \\mathrm{~cm}$ side squares. Of the possible triangular regions that can be obtained with vertices in three of these points, one has the largest area. What is this area, in $\\mathrm{cm}^{2}$?\n<image1>", "hint": "", "options": {}, "choices": []}] | 5.5 | numeric | 4 | metric geometry - area | |
144 | [{"role": "user", "question": "The picture shows one object made up of 5 identical building blocks.\n<image1>\nHow many building blocks touch exactly 3 others?", "hint": "", "options": {}, "choices": []}] | 2 | numeric | 1 | counting | |
1440 | [{"role": "user", "question": "Martinho made a bicolor kite with six pieces of a thin strip of bamboo. Two pieces were used for the diagonals, which are perpendicular. The other four pieces were used to connect the middle points on the sides of the kite, as shown in the picture. What is the ratio between the blue and y... | 1 | numeric | 4 | metric geometry - area | |
1441 | [{"role": "user", "question": "The shortest way from Atown to Cetown is through Betown. Going back by this road from Cetown to Atown, we first find the signposts on the left side of the road. Further on we find the road signs on the right side of the road. How far is it from Betown to Atown?\n<image1>", "hint": "", "op... | D | mcq | 4 | metric geometry - length | |
1442 | [{"role": "user", "question": "Toninho wants to write strictly positive and consecutive whole numbers, in the nine places of the figure, so that the sum of the three numbers in each diameter is equal to 24. What is the largest possible sum for all the nine numbers?\n<image1>", "hint": "", "options": {}, "choices": []}] | 81 | numeric | 5 | logic | |
1443 | [{"role": "user", "question": "Two circles are tangent to each other and also to two sides of a square. What is the measure of the $A \\hat{O} B$ angle, determined by three of these points of tangency, as shown in the figure?\n<image1>", "hint": "", "options": {"A": "$110^{\\circ}$", "B": "$112^{\\circ}$", "C": "$120^{... | E | mcq | 2 | metric geometry - angle | |
1444 | [{"role": "user", "question": "Ana plays with $n \\times n$ boards by placing a token in each of the cells with no common points with other cells containing tokens. In the picture beside we see how to place as many chips as possible on $5 \\times 5$ and $6 \\times 6$ boards. In this way, how many chips can Ana possibly... | D | mcq | 3 | algebra | |
1445 | [{"role": "user", "question": "The next window is a square of area $1 \\mathrm{~m}^{2}$ and is composed of four triangles, which areas, indicated in the figure, follow the ratios $3 A=4 B$ and $2 C=3 D$. A fly is placed exactly at the point where these four triangles touch each other. The fly flies directly to the side... | A | mcq | 4 | metric geometry - length | |
1446 | [{"role": "user", "question": "Julia puts the nine chips on the right in a box. She then takes one chip at a time, without looking, and notes down its digit, obtaining, at the end, a number of nine different digits. What is the probability that the number written by Julia is divisible by 45?\n<image1>", "hint": "", "op... | A | mcq | 4 | combinatorics | |
1447 | [{"role": "user", "question": "A rectangular sheet with one side of $12 \\mathrm{~cm}$ is folded along its $20 \\mathrm{~cm}$ diagonal. What is the overlapping area of the folded parts, indicated in gray in the picture beside?\n<image1>", "hint": "", "options": {"A": "$24 \\mathrm{~cm}^{2}$", "B": "$36 \\mathrm{~cm}^{2... | E | mcq | 4 | transformation geometry | |
1448 | [{"role": "user", "question": "Julia wrote four positive integers, one at each vertex of a triangular base pyramid. She calculated the sum of the numbers written on the vertices of one face and the product of the numbers written on the vertices of other two faces, obtaining 15, 20 and 30, respectively. What is the high... | 120 | numeric | 3 | algebra |
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