UQ4VLM/MathVision_preprocessed · Datasets at Hugging Face

id stringlengths 1 4	question stringlengths 31 709	options listlengths 6 6	image_path stringlengths 12 15	answer stringclasses 5 values	solution stringclasses 259 values	level int64 1 5	subject stringclasses 16 values	Answer(Option) stringclasses 5 values
900	The Mayas used points and lines to write numbers. A point stands for 1, a line for 5. Which of the following Maya-numbers stands for 17? <image1>	[ "A", "B", "C", "D", "E", "I don't know" ]	images/900.jpg	D	null	2	algebra	D
901	A digital clock shows the following time: <image1> What time is it when it uses the exactly same digits again for the first time after that? <image2>	[ "A", "B", "C", "D", "E", "I don't know" ]	images/901.jpg	C	null	3	combinatorics	C
902	The sum of the dots on opposite sides of an ordinary die is 7. Which of the following dice could be an ordinary die? <image1>	[ "A", "B", "C", "D", "E", "I don't know" ]	images/902.jpg	E	null	5	solid geometry	E
903	Which of the following geometrical figures does not appear in the big picture? <image1> <image2>	[ "A", "B", "C", "D", "E", "I don't know" ]	images/903.jpg	D	null	2	combinatorial geometry	D
906	Pia has a folding yardstick consisting of 10 equally long pieces. Which of the following figures can she not make? <image1> <image2>	[ "A", "B", "C", "D", "E", "I don't know" ]	images/906.jpg	A	null	2	combinatorial geometry	A
907	Which of the five squares has the biggest proportion of black area? <image1>	[ "A", "B", "C", "D", "E", "I don't know" ]	images/907.jpg	B	null	2	combinatorial geometry	B
908	Maxi builds towers made up of little $1 \mathrm{~cm} \times 1 \mathrm{~cm} \times 2 \mathrm{~cm}$ building blocks as can be seen in the picture. <image1> He continues to build his towers in the same way. Finally he uses 28 building blocks for one tower. What is the height of this tower?	[ "$9 \\mathrm{~cm}$", "$10 \\mathrm{~cm}$", "$11 \\mathrm{~cm}$", "$12 \\mathrm{~cm}$", "$14 \\mathrm{~cm}$", "I don't know" ]	images/908.jpg	C	null	2	algebra	C
910	Each of the nets of a cube has a line drawn on. For which net does the line form a closed loop when the net is folded up to make a cube? <image1>	[ "A", "B", "C", "D", "E", "I don't know" ]	images/910.jpg	D	null	5	descriptive geometry	D
912	4 equally heavy black pearls, 1 white pearl and a piece of iron weighing $30 \mathrm{~g}$ are placed on a beam balance as shown in the diagram. The beam balance is balanced. How heavy are 6 black and 3 white pearls altogether? <image1>	[ "$100 \\mathrm{~g}$", "$99 \\mathrm{~g}$", "$96 \\mathrm{~g}$", "$94 \\mathrm{~g}$", "$90 \\mathrm{~g}$", "I don't know" ]	images/912.jpg	E	null	2	algebra	E
914	The cardboard is folded up into a $2 \times 1 \times 1$ box. Which of the pictures does not show the box? <image1> <image2>	[ "A", "B", "C", "D", "E", "I don't know" ]	images/914.jpg	B	null	5	descriptive geometry	B
916	Which tile below completes the wall next to it? <image1> <image2>	[ "A", "B", "C", "D", "E", "I don't know" ]	images/916.jpg	E	null	2	combinatorial geometry	E
918	The board beside is formed by little white and dark squares. After a ninety-degree turn, how can this board appear? <image1> <image2>	[ "A", "B", "C", "D", "E", "I don't know" ]	images/918.jpg	D	null	1	transformation geometry	D
919	Bia has five coins as shown beside. She went to the grocery store to buy a fruit, using only three coins, without having to receive change. Among the prices of the following fruits, which one can she NOT buy? <image1>	[ "1,30", "1,35", "1,40", "1,55", "1,75", "I don't know" ]	images/919.jpg	C	null	3	combinatorics	C
923	When the bat Elisa left its cave at night, the digital clock showed <image1>. When she came back in the morning and hung herself upside down, she looked at her watch and saw <image1>. How long did she stay out of the cave?	[ "2h 48m", "2h 59m", "3h 39m", "3h 41m", "3h 49m", "I don't know" ]	images/923.jpg	D	null	3	arithmetic	D
924	Maria has exactly 9 white cubes, 9 light gray cubes and 9 dark gray cubes, all the same size. She glues all these cubes together to form a larger cube. Which of the cubes below is the one she made? <image1>	[ "A", "B", "C", "D", "E", "I don't know" ]	images/924.jpg	A	null	5	solid geometry	A
925	The following figures show five paths, indicated by the thickest lines, between the $X$ and $Y$ points. Which of these paths is the longest? <image1>	[ "A", "B", "C", "D", "E", "I don't know" ]	images/925.jpg	A	null	2	counting	A
926	Which of the following indeformable pieces of wire, when duplicated, allows to make a closed piece without crosses, with the two pieces joined by their ends? <image1>	[ "A", "B", "C", "D", "E", "I don't know" ]	images/926.jpg	B	null	2	combinatorial geometry	B
927	Amelia glues these six stickers on the faces of a cube: <image1>. The figure shows this cube in two different positions. Which adhesive is on the opposite side of the duck? <image2> <image3>	[ "(A)", "(B)", "(C)", "(D)", "(E)", "I don't know" ]	images/927.jpg	E	null	5	solid geometry	E
929	Maria puts 4 liters of water in vase I, 3 liters of water in vase II and 4 liters of water in vase III, represented on the side. Seen from the front, these three vases seem to have the same size. Which of the following images can represent the three vases, when seen from above? <image1> <image2>	[ "(A)", "(B)", "(C)", "(D)", "(E)", "I don't know" ]	images/929.jpg	A	null	5	solid geometry	A
933	Which set of weights below balances the third scale, in the picture beside? <image1> <image2>	[ "(A)", "(B)", "(C)", "(D)", "(E)", "I don't know" ]	images/933.jpg	D	null	2	algebra	D
934	Ten people order an ice cream for each one. They ask for four vanilla ice creams, three chocolate ice creams, two lemon ice creams and one mango ice cream. As a topping, they ask for four umbrellas, three cherries, two wafers and a chocolate gum, one topping for each ice cream. Since they don't want two ice creams the ...	[ "Chocolat and chocolate gum.", "Mango and cherry.", "Lemmon and wafer.", "Mango and wafer.", "Lemmon and cherry.", "I don't know" ]	images/934.jpg	E	null	2	logic	E
936	Vania has a sheet of paper divided into nine equal squares. She wants to fold the sheet as shown in the picture, initially with horizontal folds and then with vertical folds, until she leaves the colored square on top of the layers. Vania wants to write the numbers from 1 to 9 , one in each square, so that these number...	[ "$a=9, b=5, c=3$", "$a=4, b=6, c=8$", "$a=7, b=5, c=3$", "$a=3, b=5, c=7$", "$a=6, b=4, c=7$", "I don't know" ]	images/936.jpg	C	null	1	transformation geometry	C
937	The figure shows a map with some islands and how they are connected by bridges. A navigator wants to pass through each of the islands exactly once. He started at Cang Island and wants to finish at Uru Island. He has just arrived at the black island in the center of the map. In which direction must he go now to be able ...	[ "North.", "East.", "South.", "West.", "There is more than one possible choice", "I don't know" ]	images/937.jpg	C	null	2	graph theory	C
938	Which of the following solid shapes can be made with these 6 bricks? <image1> <image2>	[ "A", "B", "C", "D", "E", "I don't know" ]	images/938.jpg	D	null	2	combinatorial geometry	D
940	In the square you can see the digits from 1 to 9 <image1>. A number is created by starting at the star, following the line and writing down the digits along the line while passing. For example, the line shown represents the number 42685 <image2>. Which of the following lines represents the largest number? <image3>	[ "A", "B", "C", "D", "E", "I don't know" ]	images/940.jpg	E	null	2	algebra	E
941	Sofie wants to write the word KENGU by using letters from the boxes. She can only take one letter from each box. What letter must Sofie take from box 4? <image1>	[ "K", "E", "N", "G", "U", "I don't know" ]	images/941.jpg	D	null	2	logic	D
944	The 5 figures on the grid can only move in the directions indicated by the black arrows. Which figure can leave through gate G? <image1>	[ "A", "B", "C", "D", "E", "I don't know" ]	images/944.jpg	B	null	1	transformation geometry	B
945	Mary had a piece of paper. She folded it exactly in half. Then she folded it exactly in half again. She got this shape <image1>. Which of the shapes P, Q or R could have been the shape of her original piece of paper? <image2>	[ "only P", "only Q", "only R", "only P or Q", "any of P, Q or R", "I don't know" ]	images/945.jpg	E	null	1	transformation geometry	E
946	There is a square with line segments drawn inside it. The line segments are drawn either from the vertices or the midpoints of other line segments. We coloured $\frac{1}{8}$ of the large square. Which one is our coloring? <image1>	[ "A", "B", "C", "D", "E", "I don't know" ]	images/946.jpg	D	null	2	combinatorial geometry	D
947	The map shows three bus stations at points $A, B$ and $C$. A tour from station $A$ to the Zoo and the Port and back to $A$ is $10 \mathrm{~km}$ long. $A$ tour from station $B$ to the Park and the Zoo and back to B is $12 \mathrm{~km}$ long. A tour from station C to the Port and the Park and back to $C$ is $13 \mathrm{~...	[ "$18 \\mathrm{~km}$", "$20 \\mathrm{~km}$", "$25 \\mathrm{~km}$", "$35 \\mathrm{~km}$", "$50 \\mathrm{~km}$", "I don't know" ]	images/947.jpg	B	null	2	graph theory	B
948	Rosa wants to start at the arrow, follow the line, and get out at the other arrow. Which piece is it NOT possible to put in the middle to obtain that? <image1> <image2>	[ "A", "B", "C", "D", "E", "I don't know" ]	images/948.jpg	D	null	2	combinatorial geometry	D
950	3 rectangles of the same height are positioned as shown. The numbers within the rectangles indicate their areas in $\mathrm{cm}^{2}$. If $A B=6 \mathrm{~cm}$, how long is the distance $C D$? <image1>	[ "$7 \\mathrm{~cm}$", "$7.5 \\mathrm{~cm}$", "$8 \\mathrm{~cm}$", "$8.2 \\mathrm{~cm}$", "$8.5 \\mathrm{~cm}$", "I don't know" ]	images/950.jpg	C	null	3	metric geometry - length	C
951	A triangular pyramid is built with 10 identical balls, like this <image1>. Each ball has one of the letters A, $B, C, D$ and $E$ on it. There are 2 balls marked with each letter. The picture shows 3 side views of the pyramid. What is the letter on the ball with the question mark? <image2>	[ "A", "B", "C", "D", "E", "I don't know" ]	images/951.jpg	A	null	5	descriptive geometry	A
952	Ronja had four white tokens and Wanja had four grey tokens. They played a game in which they took turns to place one of their tokens to create two piles. Ronja placed her first token first. Which pair of piles could they not create? <image1>	[ "A", "B", "C", "D", "E", "I don't know" ]	images/952.jpg	E	null	3	combinatorics	E
953	In a railway line between the cities $X$ and $Y$, the trains can meet, traveling in opposite directions, only in one of its stretches, in which the line is double. The trains take 180 minutes to go from $X$ to $Y$ and 60 minutes to go from $Y$ to $X$, at constant speeds. On this line, a train can start from $X$ at the ...	[ "A", "B", "C", "D", "E", "I don't know" ]	images/953.jpg	B	null	2	algebra	B
955	The picture shows 3 gears with a black gear tooth on each. Which picture shows the correct position of the black teeth after the small gear has turned a full turn clockwise? <image1> <image2>	[ "A", "B", "C", "D", "E", "I don't know" ]	images/955.jpg	A	null	1	transformation geometry	A
957	My little brother has a 4-digit bike lock with the digits 0 to 9 on each part of the lock as shown. He started on the correct combination and turned each part the same amount in the same direction and now the lock shows the combination 6348. Which of the following CANNOT be the correct combination of my brother's lock?...	[ "A", "B", "C", "D", "E", "I don't know" ]	images/957.jpg	C	null	2	algebra	C
959	There are rectangular cards divided into 4 equal cells with different shapes <image1> drawn in each cell. Cards can be placed side by side only if the same shapes appear in adjacent cells on their common side. 9 cards are used to form a rectangle as shown in the figure. Which of the following cards was definitely NOT u...	[ "A", "B", "C", "D", "E", "I don't know" ]	images/959.jpg	E	null	2	logic	E
960	Six points are placed and numbered as shown on the right. Two triangles are drawn: one by connecting the even numbered points, and one by connecting the odd numbered points. Which of the following shapes is the result? <image1> <image2>	[ "A", "B", "C", "D", "E", "I don't know" ]	images/960.jpg	E	null	2	combinatorial geometry	E
961	Eva paddles around five buoys with her boat (see diagram). Which of the buoys does she paddle around in an anti-clockwise direction? <image1>	[ "1 and 4", "2, 3 and 5", "2 and 3", "1,4 and 5", "1 and 3", "I don't know" ]	images/961.jpg	E	null	4	topology	E
962	The two-sided mirrors reflect the laser beams as shown in the small picture: <image1> . At which letter does the laser beam leave the picture: <image2> ?	[ "A", "B", "C", "D", "E", "I don't know" ]	images/962.jpg	B	null	2	combinatorial geometry	B
963	In the 13th century, monks used to write numbers in the following way: <image1> For the numbers 1 to 99 they used the signs shown here or a combination of two of these signs. E.g. the number 24 was written like <image2>, the number 81 like <image3> and the number 93 like <image4>. What did the number 45 look like? <ima...	[ "A", "B", "C", "D", "E", "I don't know" ]	images/963.jpg	D	null	2	algebra	D
965	How much does this Ferris wheel need to turn so that a white gondola is on top for the first time? <image1>	[ "$\\frac{1}{2}$ turn", "$\\frac{1}{3}$ turn", "$\\frac{1}{6}$ turn", "$\\frac{1}{12}$ turn", "$\\frac{5}{6}$ turn", "I don't know" ]	images/965.jpg	D	null	3	arithmetic	D
966	The sides of the square $A B C D$ are $10 \mathrm{~cm}$ long. What is the total area of the shaded part? <image1>	[ "$40 \\mathrm{~cm}^{2}$", "$45 \\mathrm{~cm}^{2}$", "$50 \\mathrm{~cm}^{2}$", "$55 \\mathrm{~cm}^{2}$", "$60 \\mathrm{~cm}^{2}$", "I don't know" ]	images/966.jpg	C	null	3	arithmetic	C
967	Five big and four small elephants are marching along a path. Since the path is narrow the elephants cannot change their order. At the fork in the path each elephant either goes to the right or to the left. Which of the following situations cannot happen? <image1> <image2>	[ "A", "B", "C", "D", "E", "I don't know" ]	images/967.jpg	C	null	3	combinatorics	C
969	In a box-shaped water tank with dimensions $4 \mathrm{~m} \times 2 \mathrm{~m} \times 1 \mathrm{~m}$, the height of the water is $25 \mathrm{~cm}$. The tank is then turned on its side (see picture on the right). How high is the water in the tank now? <image1>	[ "$25 \\mathrm{~cm}$", "$50 \\mathrm{~cm}$", "$75 \\mathrm{~cm}$", "$1 \\mathrm{~m}$", "$1.25 \\mathrm{~m}$", "I don't know" ]	images/969.jpg	D	null	5	solid geometry	D
970	Some art work can be seen on a square-shaped transparent piece of foil. The foil is folded over twice as shown in the diagram. What does the foil look like after it has been folded over twice? <image1> <image2>	[ "A", "B", "C", "D", "E", "I don't know" ]	images/970.jpg	A	null	1	transformation geometry	A
972	Some identical glasses are stacked on top of each other. A stack with eight glasses is $42 \mathrm{~cm}$ high. A stack with two glasses is $18 \mathrm{~cm}$ high. How high is a stack with six glasses? <image1>	[ "$22 \\mathrm{~cm}$", "$24 \\mathrm{~cm}$", "$28 \\mathrm{~cm}$", "$34 \\mathrm{~cm}$", "$40 \\mathrm{~cm}$", "I don't know" ]	images/972.jpg	D	null	2	algebra	D
973	Anna has glued together several cubes of the same size to form a solid (see picture). Which of the following pictures shows a different view of this solid? <image1> <image2>	[ "A", "B", "C", "D", "E", "I don't know" ]	images/973.jpg	C	null	5	descriptive geometry	C
979	Which of the shapes cannot be split into two triangles using a single straight line? <image1>	[ "A", "B", "C", "D", "E", "I don't know" ]	images/979.jpg	A	null	2	combinatorial geometry	A
982	Four ribbons $\mathrm{M}, \mathrm{N}, \mathrm{P}$ and $\mathrm{Q}$ are wrapped around a box. <image1> In which order were they wrapped around the box?	[ "M, N, Q, P", "N, M, P, Q", "N, Q, M, P", "N, M, Q, P", "$Q, N, M, P$", "I don't know" ]	images/982.jpg	D	null	5	descriptive geometry	D
983	Alice has four jigsaw pieces. <image1> Which two can be fitted together to form a hexagon?	[ "1 and 2", "1 and 3", "2 and 3", "2 and 4", "1 and 4", "I don't know" ]	images/983.jpg	B	null	2	combinatorial geometry	B
984	A dark disc with three holes is placed on top of a dial of a watch (see diagram). Then the disc is rotated around its centre. Which numbers can be seen at the same time? <image1>	[ "4, 6 and 12", "1, 5 and 10", "2, 4 and 9", "3, 6 and 9", "5, 7 and 12", "I don't know" ]	images/984.jpg	A	null	1	transformation geometry	A
985	Jan sticks these three pieces of paper <image1> Which picture can he not obtain? <image2>	[ "A", "B", "C", "D", "E", "I don't know" ]	images/985.jpg	C	null	2	combinatorial geometry	C
986	A terrace is covered with square tiles of different sizes. The smallest tile has a perimeter of $80 \mathrm{~cm}$. A snake lay down along the edges of the tiles (see diagram). How long is the snake? <image1>	[ "$380 \\mathrm{~cm}$", "$400 \\mathrm{~cm}$", "$420 \\mathrm{~cm}$", "$440 \\mathrm{~cm}$", "$1680 \\mathrm{~cm}$", "I don't know" ]	images/986.jpg	C	null	2	combinatorial geometry	C
987	The picture of a digital watch can be seen in a mirror: <image1> Which picture of the watch can be seen in the mirror 30 minutes later?	[ "$12:22$", "$12:55$", "$15:15$", "$15:55$", "$21:21$", "I don't know" ]	images/987.jpg	D	null	1	transformation geometry	D
988	The sums of the numbers in the white and in the grey fields should be equally big. Which two numbers have to be swapped so that the sums are equally big? <image1>	[ "1 and 11", "2 and 8", "3 and 7", "4 and 13", "7 and 13", "I don't know" ]	images/988.jpg	A	null	2	algebra	A
992	A rabbit, a beaver and a kangaroo are having a competition. All three begin at the same time from the "Start" and hop in the same direction. The beaver always moves one position forwards with each jump. The rabbit always moves two positions forwards with one jump and the kangaroo always three positions. Whoever takes t...	[ "Kangaroo and rabbit", "Rabbit", "Kangaroo", "Beaver", "Kangaroo and beaver", "I don't know" ]	images/992.jpg	E	null	2	algebra	E
993	Tina draws shapes into each field of the pyramid. Each field in the second and third row contains exactly the shapes of the two fields below. Some fields are already done. Which shapes does she draw into the empty field of the bottom row? <image1> <image2>	[ "A", "B", "C", "D", "E", "I don't know" ]	images/993.jpg	D	null	2	algebra	D
994	A tower is made up of bricks that are labelled with the numbers from 1 to 50 from bottom to top. Bob uses these bricks to build a new tower. Each time he takes the two topmost bricks off the old tower and places them down on top of the new tower without changing their order (see diagram). Which two bricks lie on top of...	[ "29 and 28", "34 and 35", "29 and 26", "31 and 33", "27 and 30", "I don't know" ]	images/994.jpg	E	null	2	algebra	E
995	Martin has three cards that are labelled on both sides with a number. Martin places the three cards on the table without paying attention to back or front. He adds the three numbers that he can then see. How many different sums can Martin get that way? <image1>	[ "3", "5", "6", "9", "A different amount.", "I don't know" ]	images/995.jpg	E	null	3	combinatorics	E
996	Anna has two machines $R$ and $S$. If she places a square piece of paper in machine $R$ it is rotated $90^{\circ}$ in a clockwise direction. <image1> (Hint: Note the marking in the corner!) If she places the piece of paper in machine $S$, it gets printed on. <image2> In which order does Anna use the two machines so tha...	[ "SRRR", "RSRR", "SRSR", "RRRS", "SRRS", "I don't know" ]	images/996.jpg	B	null	1	transformation geometry	B
997	Monika wants to find a path through the labyrinth from 'Start' to 'Ziel'. She has to stick to the following rules: She is only allowed to move horizontally and vertically respectively. She has to enter every white circle exactly once but is not allowed to enter a black circle. In which direction does Monika have to mov...	[ "$\\downarrow$", "$\\uparrow$", "$\\rightarrow$", "$\\leftarrow$", "there are several possibilities", "I don't know" ]	images/997.jpg	A	null	2	graph theory	A
998	A folded napkin was cut through (see picture). What does it look like when unfolded? <image1> <image2>	[ "A", "B", "C", "D", "E", "I don't know" ]	images/998.jpg	C	null	3	transformation geometry	C
1000	Lying on a table, there is a transparent square sheet of film with the letter $\mathbf{y}$ written on it. We turn the sheet $90^{\circ}$ clockwise, then turn it over from its right side, then turn it $180^{\circ}$ counterclockwise. What do we now see? <image1>	[ "A", "B", "C", "D", "E", "I don't know" ]	images/1000.jpg	A	null	3	transformation geometry	A
1002	Two quadrates with the same size cover a circle, the radius of which is $3 \mathrm{~cm}$. Find the total area (in $\mathrm{cm}^{2}$ ) of the shaded figure. <image1>	[ "$8(\\pi-1)$", "$6(2 \\pi-1)$", "$9 \\pi-25$", "$9(\\pi-2)$", "$\\frac{6 \\pi}{5}$", "I don't know" ]	images/1002.jpg	D	null	3	metric geometry - area	D
1003	A rectangular parallelepiped was composed of 3 pieces, each consisting of 4 little cubes. Then one piece was removed (see picture). Which one? <image1> <image2>	[ "A", "B", "C", "D", "E", "I don't know" ]	images/1003.jpg	D	null	4	descriptive geometry	D
1004	In a rectangle $A B C D$, let $P, Q, R$ and $S$ be the midpoints of sides $A B, B C, C D$ and $A D$, respectively, and let $T$ be the midpoint of segment $R S$. Which fraction of the area of $A B C D$ does triangle $P Q T$ cover? <image1>	[ "$\\frac{5}{16}$", "$\\frac{1}{4}$", "$\\frac{1}{5}$", "$\\frac{1}{6}$", "$\\frac{3}{8}$", "I don't know" ]	images/1004.jpg	B	null	3	metric geometry - area	B
1006	A square is divided into 25 small squares (see the picture). Find the measure of the angle which is the sum of the angles $M A N, M B N, M C N, M D N, M E N$. <image1>	[ "30°", "45°", "60°", "75°", "90°", "I don't know" ]	images/1006.jpg	B	null	4	combinatorial geometry	B
1008	In triangle $A B C$ (see picture) $A B=A C, A E=A D$, and $\angle B A D=30^{\circ}$. What is the measure of angle $C D E$? <image1>	[ "$10^{\\circ}$", "$15^{\\circ}$", "$20^{\\circ}$", "$25^{\\circ}$", "$30^{\\circ}$", "I don't know" ]	images/1008.jpg	B	null	5	metric geometry - angle	B
1009	An equilateral triangle $A C D$ is rotated counterclockwise around point $A$. At what angle has it been rotated unen it covers equilateral triangle $A B C$ for the first time? <image1>	[ "$60^{\\circ}$", "$120^{\\circ}$", "$180^{\\circ}$", "$240^{\\circ}$", "$300^{\\circ}$", "I don't know" ]	images/1009.jpg	E	null	3	transformation geometry	E
1011	The section of a cube by a plane generates a plane figure. I have plotted this section in the development of the cube (see the picture). Can you find out what figure it is? <image1>	[ "An equilateral triangle", "A rectangle, but not a square", "A right triangle", "A square", "A hexagon", "I don't know" ]	images/1011.jpg	A	null	4	descriptive geometry	A
1017	The diagram shows the ground plan of a room. The adjacent walls are perpendicular to each other. What is the area of the room? <image1>	[ "$2 a b+a(b-a)$", "$3 a(a+b)-a^{2}$", "$3 a^{2} b$", "$3 a(b-a)+a^{2}$", "$3 a b$", "I don't know" ]	images/1017.jpg	E	null	3	metric geometry - area	E
1018	In the diagram, the five circles have the same radii and touch as shown. The square joins the centres of the four outer circles. The ratio of the area of the shaded part of all five circles to the area of the unshaded parts of the circles is: <image1>	[ "$1: 3$", "$1: 4$", "$2: 5$", "$2: 3$", "$5: 4$", "I don't know" ]	images/1018.jpg	D	null	3	metric geometry - area	D
1020	Let $a$ and $b$ be two shorter sides of the right-angled triangle. Then the sum of the diameter of the incircle and that of the circumcircle of this triangle is equal to: <image1>	[ "$\\sqrt{a^{2}+b^{2}}$", "$\\sqrt{a b}$", "$0.5(a+b)$", "$2(a+b)$", "$a+b$", "I don't know" ]	images/1020.jpg	E	null	2	metric geometry - length	E
1021	A particle moves through the first quadrant of the shown figure as follows. During the first minute it moves from the origin to $(1 ; 0)$. Thereafter it continues to follow the directions indicated in the figure, going back and forth between the positive part of the $x$ and $y$ axes, moving one unit of distance paralle...	[ "$(10 ; 0)$", "$(1 ; 11)$", "$(10 ; 11)$", "$(2 ; 10)$", "$(11 ; 11)$", "I don't know" ]	images/1021.jpg	A	null	4	algebra	A
1022	The point $O$ is the centre of a regular pentagon. How much of the pentagon is shaded? <image1>	[ "$10 \\%$", "$20 \\%$", "$25 \\%$", "$30 \\%$", "$40 \\%$", "I don't know" ]	images/1022.jpg	D	null	3	metric geometry - area	D
1023	Which of the following nets has a cube in the right picture? <image1> <image2>	[ "A", "B", "C", "D", "E", "I don't know" ]	images/1023.jpg	E	null	4	descriptive geometry	E
1024	The solid in the picture is created from two cubes. The small cube with edges $1 \mathrm{~cm}$ long is placed on the top of a bigger cube with edges $3 \mathrm{~cm}$ long. What is the surface area of this solid? <image1>	[ "$56 \\mathrm{~cm}^{2}$", "$58 \\mathrm{~cm}^{2}$", "$59 \\mathrm{~cm}^{2}$", "$60 \\mathrm{~cm}^{2}$", "$64 \\mathrm{~cm}^{2}$", "I don't know" ]	images/1024.jpg	B	null	4	solid geometry	B
1029	The first row shows 11 cards, each with two letters. The second row shows rearangement of the cards. Which of the following could appear on the bottom line of the second row? <image1>	[ "ANJAMKILIOR", "RLIIMKOJNAA", "JANAMKILIRO", "RAONJMILIKA", "ANMAIKOLIRJ", "I don't know" ]	images/1029.jpg	E	null	4	algebra	E
1033	There are six identical circles in the picture. The circles touch the sides of a large rectangle and one another as well. The vertices of the small rectangle lie in the centres of the four circles, as illustrated. The perimeter of the small rectangle is $60 \mathrm{~cm}$. What is the perimeter of the large rectangle? <...	[ "$160 \\mathrm{~cm}$", "$140 \\mathrm{~cm}$", "$120 \\mathrm{~cm}$", "$100 \\mathrm{~cm}$", "$80 \\mathrm{~cm}$", "I don't know" ]	images/1033.jpg	D	null	2	metric geometry - length	D
1034	$A B C$ and $C D E$ are equal equilateral triangles. If $\angle A C D=80^{\circ}$, what is $\angle A B D$? <image1>	[ "$25^{\\circ}$", "$30^{\\circ}$", "$35^{\\circ}$", "$40^{\\circ}$", "$45^{\\circ}$", "I don't know" ]	images/1034.jpg	D	null	5	metric geometry - angle	D
1036	Which of the following objects can be obtained by rotating in space the grey object? <image1> <image2>	[ "W and Y", "X and Z", "Only Y", "None of these", "W, X ir Y", "I don't know" ]	images/1036.jpg	A	null	4	solid geometry	A
1038	In the picture there is a square tile with two fourths of a circle. The radius of every fourth is half the side of the tile and its length equals $5 \mathrm{dm}$. We form a large square from 16 such tiles and try to get the longest unbroken curve consisting of the fourths. How long can this continuous curve be at most?...	[ "$75 \\mathrm{dm}$", "$100 \\mathrm{dm}$", "$105 \\mathrm{dm}$", "$110 \\mathrm{dm}$", "$80 \\mathrm{dm}$", "I don't know" ]	images/1038.jpg	D	null	4	combinatorial geometry	D
1041	Three lines intersect at one point. Two angles are given in the figure. How many degrees does the grey angle have? <image1>	[ "$52^{\\circ}$", "$53^{\\circ}$", "$54^{\\circ}$", "$55^{\\circ}$", "$56^{\\circ}$", "I don't know" ]	images/1041.jpg	A	null	5	metric geometry - angle	A
1043	Four tangent congruent circles of radius $6 \mathrm{~cm}$ are inscribed in a rectangle. <image1> If $P$ is a vertex and $Q$ and $R$ are the points of tangency, what is the area of triangle $P Q R$?	[ "$27 \\mathrm{~cm}^{2}$", "$45 \\mathrm{~cm}^{2}$", "$54 \\mathrm{~cm}^{2}$", "$108 \\mathrm{~cm}^{2}$", "$180 \\mathrm{~cm}^{2}$", "I don't know" ]	images/1043.jpg	D	null	3	metric geometry - area	D
1044	In an isosceles triangle $A B C(A B=A C)$, the bisector $C D$ of the angle $C$ is equal to the base $B C$. Then the angle $C D A$ is equal to <image1>	[ "$90^{\\circ}$", "$100^{\\circ}$", "$108^{\\circ}$", "$120^{\\circ}$", "Impossible to determine", "I don't know" ]	images/1044.jpg	C	null	5	metric geometry - angle	C
1047	The star shown in the picture is made by fitting together 12 congruent equilateral triangles. The perimeter of the star is $36 \mathrm{~cm}$. What is the perimeter of the grey hexagon? <image1>	[ "$6 \\mathrm{~cm}$", "$12 \\mathrm{~cm}$", "$18 \\mathrm{~cm}$", "$24 \\mathrm{~cm}$", "$30 \\mathrm{~cm}$", "I don't know" ]	images/1047.jpg	C	null	4	combinatorial geometry	C
1048	In the picture the large square has an area of 1. What is the area of the small black square? <image1>	[ "$\\frac{1}{100}$", "$\\frac{1}{300}$", "$\\frac{1}{600}$", "$\\frac{1}{900}$", "$\\frac{1}{1000}$", "I don't know" ]	images/1048.jpg	D	null	5	arithmetic	D
1049	In the diagram QSR is a straight line. $\angle \mathrm{QPS}=12^{\circ}$ and $\mathrm{PQ}=\mathrm{PS}=\mathrm{RS}$. How big is $\angle \mathrm{QPR}$? <image1>	[ "$36^{\\circ}$", "$42^{\\circ}$", "$54^{\\circ}$", "$60^{\\circ}$", "$84^{\\circ}$", "I don't know" ]	images/1049.jpg	C	null	5	metric geometry - angle	C
1050	Which of the following is made using more than one piece of string? <image1>	[ "I, III, IV and V", "I, III and V", "III, IV and V", "all", "None of these answers", "I don't know" ]	images/1050.jpg	B	null	3	topology	B
1052	What fraction of the largest square is grey? <image1>	[ "$\\frac{1}{4}$", "$\\frac{1}{5}$", "$\\frac{2}{5}$", "$\\frac{3}{8}$", "$\\frac{1}{3}$", "I don't know" ]	images/1052.jpg	A	null	3	metric geometry - area	A
1054	We want to paint each square in the grid with the colours P, Q, R and S, so that neighbouring squares always have different colours. (Squares which share the same corner point also count as neighbouring.) Some of the squares are already painted. In which colour(s) could the grey square be painted? <image1>	[ "only Q", "only R", "only S", "either R or S", "it is not possible.", "I don't know" ]	images/1054.jpg	D	null	3	graph theory	D
1055	The diagram opposite shows a regular nonagon. What is the size of the angle marked $\mathrm{X}$? <image1>	[ "$40^{\\circ}$", "$45^{\\circ}$", "$50^{\\circ}$", "$55^{\\circ}$", "$60^{\\circ}$", "I don't know" ]	images/1055.jpg	E	null	5	metric geometry - angle	E
1058	The fractions $\frac{1}{3}$ und $\frac{1}{5}$ are shown on the number line. In which position should $\frac{1}{4}$ be shown? <image1>	[ "a", "b", "c", "d", "e", "I don't know" ]	images/1058.jpg	A	null	4	algebra	A
1059	A cube is cut in three directions as shown, to produce eight cuboids (each cut is parallel to one of the faces of the cube). What is the ratio of the total surface area of the eight cuboids to the surface area of the original cube? <image1>	[ "1:1", "4:3", "3:2", "2:1", "4:1", "I don't know" ]	images/1059.jpg	D	null	4	solid geometry	D
1061	The perimeter of the figure pictured on the right is...... <image1>	[ "$3 a+4 b$", "$3 a+8 b$", "$6 a+4 b$", "$6 a+6 b$", "$6 a+8 b$", "I don't know" ]	images/1061.jpg	E	null	2	metric geometry - length	E
1062	Martina draws the six cornerpoints of a regular hexagon and then connects some of them to obtain a geometric figure. Which of the following figures cannot be generated? <image1>	[ "trapezium", "right angled triangle", "square", "kite", "obtuse triangle", "I don't know" ]	images/1062.jpg	C	null	4	combinatorial geometry	C
1064	In the quadrilateral $\mathrm{ABCD}, \mathrm{AD}=\mathrm{BC}, \angle \mathrm{DAC}=50^{\circ}$, $\angle \mathrm{DCA}=65^{\circ}$ and $\angle \mathrm{ACB}=70^{\circ}$. How big is $\angle \mathrm{ABC}$? <image1>	[ "$50^{\\circ}$", "$55^{\\circ}$", "$60^{\\circ}$", "$65^{\\circ}$", "It is not clear.", "I don't know" ]	images/1064.jpg	B	null	5	metric geometry - angle	B
1065	Andrea wraps a band around a piece of wood. She then turns the wood around as pictured. What does the wood now look like? <image1> <image2>	[ "A", "B", "C", "D", "E", "I don't know" ]	images/1065.jpg	B	null	3	transformation geometry	B

900

The Mayas used points and lines to write numbers. A point stands for 1, a line for 5. Which of the following Maya-numbers stands for 17? <image1>

[ "A", "B", "C", "D", "E", "I don't know" ]

images/900.jpg

D

null

2

algebra

D

901

A digital clock shows the following time: <image1> What time is it when it uses the exactly same digits again for the first time after that? <image2>

[ "A", "B", "C", "D", "E", "I don't know" ]

images/901.jpg

C

null

3

combinatorics

C

902

The sum of the dots on opposite sides of an ordinary die is 7. Which of the following dice could be an ordinary die? <image1>

[ "A", "B", "C", "D", "E", "I don't know" ]

images/902.jpg

E

null

5

solid geometry

E

903

Which of the following geometrical figures does not appear in the big picture? <image1> <image2>

[ "A", "B", "C", "D", "E", "I don't know" ]

images/903.jpg

D

null

2

combinatorial geometry

D

906

Pia has a folding yardstick consisting of 10 equally long pieces. Which of the following figures can she not make? <image1> <image2>

[ "A", "B", "C", "D", "E", "I don't know" ]

images/906.jpg

A

null

2

combinatorial geometry

A

907

Which of the five squares has the biggest proportion of black area? <image1>

[ "A", "B", "C", "D", "E", "I don't know" ]

images/907.jpg

B

null

2

combinatorial geometry

B

908

Maxi builds towers made up of little $1 \mathrm{~cm} \times 1 \mathrm{~cm} \times 2 \mathrm{~cm}$ building blocks as can be seen in the picture. <image1> He continues to build his towers in the same way. Finally he uses 28 building blocks for one tower. What is the height of this tower?

[ "$9 \\mathrm{~cm}$", "$10 \\mathrm{~cm}$", "$11 \\mathrm{~cm}$", "$12 \\mathrm{~cm}$", "$14 \\mathrm{~cm}$", "I don't know" ]

images/908.jpg

C

null

2

algebra

C

910

Each of the nets of a cube has a line drawn on. For which net does the line form a closed loop when the net is folded up to make a cube? <image1>

[ "A", "B", "C", "D", "E", "I don't know" ]

images/910.jpg

D

null

5

descriptive geometry

D

912

4 equally heavy black pearls, 1 white pearl and a piece of iron weighing $30 \mathrm{~g}$ are placed on a beam balance as shown in the diagram. The beam balance is balanced. How heavy are 6 black and 3 white pearls altogether? <image1>

[ "$100 \\mathrm{~g}$", "$99 \\mathrm{~g}$", "$96 \\mathrm{~g}$", "$94 \\mathrm{~g}$", "$90 \\mathrm{~g}$", "I don't know" ]

images/912.jpg

E

null

2

algebra

E

914

The cardboard is folded up into a $2 \times 1 \times 1$ box. Which of the pictures does not show the box? <image1> <image2>

[ "A", "B", "C", "D", "E", "I don't know" ]

images/914.jpg

B

null

5

descriptive geometry

B

916

Which tile below completes the wall next to it? <image1> <image2>

[ "A", "B", "C", "D", "E", "I don't know" ]

images/916.jpg

E

null

2

combinatorial geometry

E

918

The board beside is formed by little white and dark squares. After a ninety-degree turn, how can this board appear? <image1> <image2>

[ "A", "B", "C", "D", "E", "I don't know" ]

images/918.jpg

D

null

1

transformation geometry

D

919

Bia has five coins as shown beside. She went to the grocery store to buy a fruit, using only three coins, without having to receive change. Among the prices of the following fruits, which one can she NOT buy? <image1>

[ "1,30", "1,35", "1,40", "1,55", "1,75", "I don't know" ]

images/919.jpg

C

null

3

combinatorics

C

923

When the bat Elisa left its cave at night, the digital clock showed <image1>. When she came back in the morning and hung herself upside down, she looked at her watch and saw <image1>. How long did she stay out of the cave?

[ "2h 48m", "2h 59m", "3h 39m", "3h 41m", "3h 49m", "I don't know" ]

images/923.jpg

D

null

3

arithmetic

D

924

Maria has exactly 9 white cubes, 9 light gray cubes and 9 dark gray cubes, all the same size. She glues all these cubes together to form a larger cube. Which of the cubes below is the one she made? <image1>

[ "A", "B", "C", "D", "E", "I don't know" ]

images/924.jpg

A

null

5

solid geometry

A

925

The following figures show five paths, indicated by the thickest lines, between the $X$ and $Y$ points. Which of these paths is the longest? <image1>

[ "A", "B", "C", "D", "E", "I don't know" ]

images/925.jpg

A

null

2

counting

A

926

Which of the following indeformable pieces of wire, when duplicated, allows to make a closed piece without crosses, with the two pieces joined by their ends? <image1>

[ "A", "B", "C", "D", "E", "I don't know" ]

images/926.jpg

B

null

2

combinatorial geometry

B

927

Amelia glues these six stickers on the faces of a cube: <image1>. The figure shows this cube in two different positions. Which adhesive is on the opposite side of the duck? <image2> <image3>

[ "(A)", "(B)", "(C)", "(D)", "(E)", "I don't know" ]

images/927.jpg

E

null

5

solid geometry

E

929

Maria puts 4 liters of water in vase I, 3 liters of water in vase II and 4 liters of water in vase III, represented on the side. Seen from the front, these three vases seem to have the same size. Which of the following images can represent the three vases, when seen from above? <image1> <image2>

[ "(A)", "(B)", "(C)", "(D)", "(E)", "I don't know" ]

images/929.jpg

A

null

5

solid geometry

A

933

Which set of weights below balances the third scale, in the picture beside? <image1> <image2>

[ "(A)", "(B)", "(C)", "(D)", "(E)", "I don't know" ]

images/933.jpg

D

null

2

algebra

D

934

Ten people order an ice cream for each one. They ask for four vanilla ice creams, three chocolate ice creams, two lemon ice creams and one mango ice cream. As a topping, they ask for four umbrellas, three cherries, two wafers and a chocolate gum, one topping for each ice cream. Since they don't want two ice creams the ...

[ "Chocolat and chocolate gum.", "Mango and cherry.", "Lemmon and wafer.", "Mango and wafer.", "Lemmon and cherry.", "I don't know" ]

images/934.jpg

E

null

2

logic

E

936

Vania has a sheet of paper divided into nine equal squares. She wants to fold the sheet as shown in the picture, initially with horizontal folds and then with vertical folds, until she leaves the colored square on top of the layers. Vania wants to write the numbers from 1 to 9 , one in each square, so that these number...

[ "$a=9, b=5, c=3$", "$a=4, b=6, c=8$", "$a=7, b=5, c=3$", "$a=3, b=5, c=7$", "$a=6, b=4, c=7$", "I don't know" ]

images/936.jpg

C

null

1

transformation geometry

C

937

The figure shows a map with some islands and how they are connected by bridges. A navigator wants to pass through each of the islands exactly once. He started at Cang Island and wants to finish at Uru Island. He has just arrived at the black island in the center of the map. In which direction must he go now to be able ...

[ "North.", "East.", "South.", "West.", "There is more than one possible choice", "I don't know" ]

images/937.jpg

C

null

2

graph theory

C

938

Which of the following solid shapes can be made with these 6 bricks? <image1> <image2>

[ "A", "B", "C", "D", "E", "I don't know" ]

images/938.jpg

D

null

2

combinatorial geometry

D

940

In the square you can see the digits from 1 to 9 <image1>. A number is created by starting at the star, following the line and writing down the digits along the line while passing. For example, the line shown represents the number 42685 <image2>. Which of the following lines represents the largest number? <image3>

[ "A", "B", "C", "D", "E", "I don't know" ]

images/940.jpg

E

null

2

algebra

E

941

Sofie wants to write the word KENGU by using letters from the boxes. She can only take one letter from each box. What letter must Sofie take from box 4? <image1>

[ "K", "E", "N", "G", "U", "I don't know" ]

images/941.jpg

D

null

2

logic

D

944

The 5 figures on the grid can only move in the directions indicated by the black arrows. Which figure can leave through gate G? <image1>

[ "A", "B", "C", "D", "E", "I don't know" ]

images/944.jpg

B

null

1

transformation geometry

B

945

Mary had a piece of paper. She folded it exactly in half. Then she folded it exactly in half again. She got this shape <image1>. Which of the shapes P, Q or R could have been the shape of her original piece of paper? <image2>

[ "only P", "only Q", "only R", "only P or Q", "any of P, Q or R", "I don't know" ]

images/945.jpg

E

null

1

transformation geometry

E

946

There is a square with line segments drawn inside it. The line segments are drawn either from the vertices or the midpoints of other line segments. We coloured $\frac{1}{8}$ of the large square. Which one is our coloring? <image1>

[ "A", "B", "C", "D", "E", "I don't know" ]

images/946.jpg

D

null

2

combinatorial geometry

D

947

The map shows three bus stations at points $A, B$ and $C$. A tour from station $A$ to the Zoo and the Port and back to $A$ is $10 \mathrm{~km}$ long. $A$ tour from station $B$ to the Park and the Zoo and back to B is $12 \mathrm{~km}$ long. A tour from station C to the Port and the Park and back to $C$ is $13 \mathrm{~...

[ "$18 \\mathrm{~km}$", "$20 \\mathrm{~km}$", "$25 \\mathrm{~km}$", "$35 \\mathrm{~km}$", "$50 \\mathrm{~km}$", "I don't know" ]

images/947.jpg

B

null

2

graph theory

B

948

Rosa wants to start at the arrow, follow the line, and get out at the other arrow. Which piece is it NOT possible to put in the middle to obtain that? <image1> <image2>

[ "A", "B", "C", "D", "E", "I don't know" ]

images/948.jpg

D

null

2

combinatorial geometry

D

950

3 rectangles of the same height are positioned as shown. The numbers within the rectangles indicate their areas in $\mathrm{cm}^{2}$. If $A B=6 \mathrm{~cm}$, how long is the distance $C D$? <image1>

[ "$7 \\mathrm{~cm}$", "$7.5 \\mathrm{~cm}$", "$8 \\mathrm{~cm}$", "$8.2 \\mathrm{~cm}$", "$8.5 \\mathrm{~cm}$", "I don't know" ]

images/950.jpg

C

null

3

metric geometry - length

C

951

A triangular pyramid is built with 10 identical balls, like this <image1>. Each ball has one of the letters A, $B, C, D$ and $E$ on it. There are 2 balls marked with each letter. The picture shows 3 side views of the pyramid. What is the letter on the ball with the question mark? <image2>

[ "A", "B", "C", "D", "E", "I don't know" ]

images/951.jpg

A

null

5

descriptive geometry

A

952

Ronja had four white tokens and Wanja had four grey tokens. They played a game in which they took turns to place one of their tokens to create two piles. Ronja placed her first token first. Which pair of piles could they not create? <image1>

[ "A", "B", "C", "D", "E", "I don't know" ]

images/952.jpg

E

null

3

combinatorics

E

953

In a railway line between the cities $X$ and $Y$, the trains can meet, traveling in opposite directions, only in one of its stretches, in which the line is double. The trains take 180 minutes to go from $X$ to $Y$ and 60 minutes to go from $Y$ to $X$, at constant speeds. On this line, a train can start from $X$ at the ...

[ "A", "B", "C", "D", "E", "I don't know" ]

images/953.jpg

B

null

2

algebra

B

955

The picture shows 3 gears with a black gear tooth on each. Which picture shows the correct position of the black teeth after the small gear has turned a full turn clockwise? <image1> <image2>

[ "A", "B", "C", "D", "E", "I don't know" ]

images/955.jpg

A

null

1

transformation geometry

A

957

My little brother has a 4-digit bike lock with the digits 0 to 9 on each part of the lock as shown. He started on the correct combination and turned each part the same amount in the same direction and now the lock shows the combination 6348. Which of the following CANNOT be the correct combination of my brother's lock?...

[ "A", "B", "C", "D", "E", "I don't know" ]

images/957.jpg

C

null

2

algebra

C

959

There are rectangular cards divided into 4 equal cells with different shapes <image1> drawn in each cell. Cards can be placed side by side only if the same shapes appear in adjacent cells on their common side. 9 cards are used to form a rectangle as shown in the figure. Which of the following cards was definitely NOT u...

[ "A", "B", "C", "D", "E", "I don't know" ]

images/959.jpg

E

null

2

logic

E

960

Six points are placed and numbered as shown on the right. Two triangles are drawn: one by connecting the even numbered points, and one by connecting the odd numbered points. Which of the following shapes is the result? <image1> <image2>

[ "A", "B", "C", "D", "E", "I don't know" ]

images/960.jpg

E

null

2

combinatorial geometry

E

961

Eva paddles around five buoys with her boat (see diagram). Which of the buoys does she paddle around in an anti-clockwise direction? <image1>

[ "1 and 4", "2, 3 and 5", "2 and 3", "1,4 and 5", "1 and 3", "I don't know" ]

images/961.jpg

E

null

4

topology

E

962

The two-sided mirrors reflect the laser beams as shown in the small picture: <image1> . At which letter does the laser beam leave the picture: <image2> ?

[ "A", "B", "C", "D", "E", "I don't know" ]

images/962.jpg

B

null

2

combinatorial geometry

B

963

In the 13th century, monks used to write numbers in the following way: <image1> For the numbers 1 to 99 they used the signs shown here or a combination of two of these signs. E.g. the number 24 was written like <image2>, the number 81 like <image3> and the number 93 like <image4>. What did the number 45 look like? <ima...

[ "A", "B", "C", "D", "E", "I don't know" ]

images/963.jpg

D

null

2

algebra

D

965

How much does this Ferris wheel need to turn so that a white gondola is on top for the first time? <image1>

[ "$\\frac{1}{2}$ turn", "$\\frac{1}{3}$ turn", "$\\frac{1}{6}$ turn", "$\\frac{1}{12}$ turn", "$\\frac{5}{6}$ turn", "I don't know" ]

images/965.jpg

D

null

3

arithmetic

D

966

The sides of the square $A B C D$ are $10 \mathrm{~cm}$ long. What is the total area of the shaded part? <image1>

[ "$40 \\mathrm{~cm}^{2}$", "$45 \\mathrm{~cm}^{2}$", "$50 \\mathrm{~cm}^{2}$", "$55 \\mathrm{~cm}^{2}$", "$60 \\mathrm{~cm}^{2}$", "I don't know" ]

images/966.jpg

C

null

3

arithmetic

C

967

Five big and four small elephants are marching along a path. Since the path is narrow the elephants cannot change their order. At the fork in the path each elephant either goes to the right or to the left. Which of the following situations cannot happen? <image1> <image2>

[ "A", "B", "C", "D", "E", "I don't know" ]

images/967.jpg

C

null

3

combinatorics

C

969

In a box-shaped water tank with dimensions $4 \mathrm{~m} \times 2 \mathrm{~m} \times 1 \mathrm{~m}$, the height of the water is $25 \mathrm{~cm}$. The tank is then turned on its side (see picture on the right). How high is the water in the tank now? <image1>

[ "$25 \\mathrm{~cm}$", "$50 \\mathrm{~cm}$", "$75 \\mathrm{~cm}$", "$1 \\mathrm{~m}$", "$1.25 \\mathrm{~m}$", "I don't know" ]

images/969.jpg

D

null

5

solid geometry

D

970

Some art work can be seen on a square-shaped transparent piece of foil. The foil is folded over twice as shown in the diagram. What does the foil look like after it has been folded over twice? <image1> <image2>

[ "A", "B", "C", "D", "E", "I don't know" ]

images/970.jpg

A

null

1

transformation geometry

A

972

Some identical glasses are stacked on top of each other. A stack with eight glasses is $42 \mathrm{~cm}$ high. A stack with two glasses is $18 \mathrm{~cm}$ high. How high is a stack with six glasses? <image1>

[ "$22 \\mathrm{~cm}$", "$24 \\mathrm{~cm}$", "$28 \\mathrm{~cm}$", "$34 \\mathrm{~cm}$", "$40 \\mathrm{~cm}$", "I don't know" ]

images/972.jpg

D

null

2

algebra

D

973

Anna has glued together several cubes of the same size to form a solid (see picture). Which of the following pictures shows a different view of this solid? <image1> <image2>

[ "A", "B", "C", "D", "E", "I don't know" ]

images/973.jpg

C

null

5

descriptive geometry

C

979

Which of the shapes cannot be split into two triangles using a single straight line? <image1>

[ "A", "B", "C", "D", "E", "I don't know" ]

images/979.jpg

A

null

2

combinatorial geometry

A

982

Four ribbons $\mathrm{M}, \mathrm{N}, \mathrm{P}$ and $\mathrm{Q}$ are wrapped around a box. <image1> In which order were they wrapped around the box?

[ "M, N, Q, P", "N, M, P, Q", "N, Q, M, P", "N, M, Q, P", "$Q, N, M, P$", "I don't know" ]

images/982.jpg

D

null

5

descriptive geometry

D

983

Alice has four jigsaw pieces. <image1> Which two can be fitted together to form a hexagon?

[ "1 and 2", "1 and 3", "2 and 3", "2 and 4", "1 and 4", "I don't know" ]

images/983.jpg

B

null

2

combinatorial geometry

B

984

A dark disc with three holes is placed on top of a dial of a watch (see diagram). Then the disc is rotated around its centre. Which numbers can be seen at the same time? <image1>

[ "4, 6 and 12", "1, 5 and 10", "2, 4 and 9", "3, 6 and 9", "5, 7 and 12", "I don't know" ]

images/984.jpg

A

null

1

transformation geometry

A

985

Jan sticks these three pieces of paper <image1> Which picture can he not obtain? <image2>

[ "A", "B", "C", "D", "E", "I don't know" ]

images/985.jpg

C

null

2

combinatorial geometry

C

986

A terrace is covered with square tiles of different sizes. The smallest tile has a perimeter of $80 \mathrm{~cm}$. A snake lay down along the edges of the tiles (see diagram). How long is the snake? <image1>

[ "$380 \\mathrm{~cm}$", "$400 \\mathrm{~cm}$", "$420 \\mathrm{~cm}$", "$440 \\mathrm{~cm}$", "$1680 \\mathrm{~cm}$", "I don't know" ]

images/986.jpg

C

null

2

combinatorial geometry

C

987

The picture of a digital watch can be seen in a mirror: <image1> Which picture of the watch can be seen in the mirror 30 minutes later?

[ "$12:22$", "$12:55$", "$15:15$", "$15:55$", "$21:21$", "I don't know" ]

images/987.jpg

D

null

1

transformation geometry

D

988

The sums of the numbers in the white and in the grey fields should be equally big. Which two numbers have to be swapped so that the sums are equally big? <image1>

[ "1 and 11", "2 and 8", "3 and 7", "4 and 13", "7 and 13", "I don't know" ]

images/988.jpg

A

null

2

algebra

A

992

A rabbit, a beaver and a kangaroo are having a competition. All three begin at the same time from the "Start" and hop in the same direction. The beaver always moves one position forwards with each jump. The rabbit always moves two positions forwards with one jump and the kangaroo always three positions. Whoever takes t...

[ "Kangaroo and rabbit", "Rabbit", "Kangaroo", "Beaver", "Kangaroo and beaver", "I don't know" ]

images/992.jpg

E

null

2

algebra

E

993

Tina draws shapes into each field of the pyramid. Each field in the second and third row contains exactly the shapes of the two fields below. Some fields are already done. Which shapes does she draw into the empty field of the bottom row? <image1> <image2>

[ "A", "B", "C", "D", "E", "I don't know" ]

images/993.jpg

D

null

2

algebra

D

994

A tower is made up of bricks that are labelled with the numbers from 1 to 50 from bottom to top. Bob uses these bricks to build a new tower. Each time he takes the two topmost bricks off the old tower and places them down on top of the new tower without changing their order (see diagram). Which two bricks lie on top of...

[ "29 and 28", "34 and 35", "29 and 26", "31 and 33", "27 and 30", "I don't know" ]

images/994.jpg

E

null

2

algebra

E

995

Martin has three cards that are labelled on both sides with a number. Martin places the three cards on the table without paying attention to back or front. He adds the three numbers that he can then see. How many different sums can Martin get that way? <image1>

[ "3", "5", "6", "9", "A different amount.", "I don't know" ]

images/995.jpg

E

null

3

combinatorics

E

996

Anna has two machines $R$ and $S$. If she places a square piece of paper in machine $R$ it is rotated $90^{\circ}$ in a clockwise direction. <image1> (Hint: Note the marking in the corner!) If she places the piece of paper in machine $S$, it gets printed on. <image2> In which order does Anna use the two machines so tha...

[ "SRRR", "RSRR", "SRSR", "RRRS", "SRRS", "I don't know" ]

images/996.jpg

B

null

1

transformation geometry

B

997

Monika wants to find a path through the labyrinth from 'Start' to 'Ziel'. She has to stick to the following rules: She is only allowed to move horizontally and vertically respectively. She has to enter every white circle exactly once but is not allowed to enter a black circle. In which direction does Monika have to mov...

[ "$\\downarrow$", "$\\uparrow$", "$\\rightarrow$", "$\\leftarrow$", "there are several possibilities", "I don't know" ]

images/997.jpg

A

null

2

graph theory

A

998

A folded napkin was cut through (see picture). What does it look like when unfolded? <image1> <image2>

[ "A", "B", "C", "D", "E", "I don't know" ]

images/998.jpg

C

null

3

transformation geometry

C

1000

Lying on a table, there is a transparent square sheet of film with the letter $\mathbf{y}$ written on it. We turn the sheet $90^{\circ}$ clockwise, then turn it over from its right side, then turn it $180^{\circ}$ counterclockwise. What do we now see? <image1>

[ "A", "B", "C", "D", "E", "I don't know" ]

images/1000.jpg

A

null

3

transformation geometry

A

1002

Two quadrates with the same size cover a circle, the radius of which is $3 \mathrm{~cm}$. Find the total area (in $\mathrm{cm}^{2}$ ) of the shaded figure. <image1>

[ "$8(\\pi-1)$", "$6(2 \\pi-1)$", "$9 \\pi-25$", "$9(\\pi-2)$", "$\\frac{6 \\pi}{5}$", "I don't know" ]

images/1002.jpg

D

null

3

metric geometry - area

D

1003

A rectangular parallelepiped was composed of 3 pieces, each consisting of 4 little cubes. Then one piece was removed (see picture). Which one? <image1> <image2>

[ "A", "B", "C", "D", "E", "I don't know" ]

images/1003.jpg

D

null

4

descriptive geometry

D

1004

In a rectangle $A B C D$, let $P, Q, R$ and $S$ be the midpoints of sides $A B, B C, C D$ and $A D$, respectively, and let $T$ be the midpoint of segment $R S$. Which fraction of the area of $A B C D$ does triangle $P Q T$ cover? <image1>

[ "$\\frac{5}{16}$", "$\\frac{1}{4}$", "$\\frac{1}{5}$", "$\\frac{1}{6}$", "$\\frac{3}{8}$", "I don't know" ]

images/1004.jpg

B

null

3

metric geometry - area

B

1006

A square is divided into 25 small squares (see the picture). Find the measure of the angle which is the sum of the angles $M A N, M B N, M C N, M D N, M E N$. <image1>

[ "30°", "45°", "60°", "75°", "90°", "I don't know" ]

images/1006.jpg

B

null

4

combinatorial geometry

B

1008

In triangle $A B C$ (see picture) $A B=A C, A E=A D$, and $\angle B A D=30^{\circ}$. What is the measure of angle $C D E$? <image1>

[ "$10^{\\circ}$", "$15^{\\circ}$", "$20^{\\circ}$", "$25^{\\circ}$", "$30^{\\circ}$", "I don't know" ]

images/1008.jpg

B

null

5

metric geometry - angle

B

1009

An equilateral triangle $A C D$ is rotated counterclockwise around point $A$. At what angle has it been rotated unen it covers equilateral triangle $A B C$ for the first time? <image1>

[ "$60^{\\circ}$", "$120^{\\circ}$", "$180^{\\circ}$", "$240^{\\circ}$", "$300^{\\circ}$", "I don't know" ]

images/1009.jpg

E

null

3

transformation geometry

E

1011

The section of a cube by a plane generates a plane figure. I have plotted this section in the development of the cube (see the picture). Can you find out what figure it is? <image1>

[ "An equilateral triangle", "A rectangle, but not a square", "A right triangle", "A square", "A hexagon", "I don't know" ]

images/1011.jpg

A

null

4

descriptive geometry

A

1017

The diagram shows the ground plan of a room. The adjacent walls are perpendicular to each other. What is the area of the room? <image1>

[ "$2 a b+a(b-a)$", "$3 a(a+b)-a^{2}$", "$3 a^{2} b$", "$3 a(b-a)+a^{2}$", "$3 a b$", "I don't know" ]

images/1017.jpg

E

null

3

metric geometry - area

E

1018

In the diagram, the five circles have the same radii and touch as shown. The square joins the centres of the four outer circles. The ratio of the area of the shaded part of all five circles to the area of the unshaded parts of the circles is: <image1>

[ "$1: 3$", "$1: 4$", "$2: 5$", "$2: 3$", "$5: 4$", "I don't know" ]

images/1018.jpg

D

null

3

metric geometry - area

D

1020

Let $a$ and $b$ be two shorter sides of the right-angled triangle. Then the sum of the diameter of the incircle and that of the circumcircle of this triangle is equal to: <image1>

[ "$\\sqrt{a^{2}+b^{2}}$", "$\\sqrt{a b}$", "$0.5(a+b)$", "$2(a+b)$", "$a+b$", "I don't know" ]

images/1020.jpg

E

null

2

metric geometry - length

E

1021

A particle moves through the first quadrant of the shown figure as follows. During the first minute it moves from the origin to $(1 ; 0)$. Thereafter it continues to follow the directions indicated in the figure, going back and forth between the positive part of the $x$ and $y$ axes, moving one unit of distance paralle...

[ "$(10 ; 0)$", "$(1 ; 11)$", "$(10 ; 11)$", "$(2 ; 10)$", "$(11 ; 11)$", "I don't know" ]

images/1021.jpg

A

null

4

algebra

A

1022

The point $O$ is the centre of a regular pentagon. How much of the pentagon is shaded? <image1>

[ "$10 \\%$", "$20 \\%$", "$25 \\%$", "$30 \\%$", "$40 \\%$", "I don't know" ]

images/1022.jpg

D

null

3

metric geometry - area

D

1023

Which of the following nets has a cube in the right picture? <image1> <image2>

[ "A", "B", "C", "D", "E", "I don't know" ]

images/1023.jpg

E

null

4

descriptive geometry

E

1024

The solid in the picture is created from two cubes. The small cube with edges $1 \mathrm{~cm}$ long is placed on the top of a bigger cube with edges $3 \mathrm{~cm}$ long. What is the surface area of this solid? <image1>

[ "$56 \\mathrm{~cm}^{2}$", "$58 \\mathrm{~cm}^{2}$", "$59 \\mathrm{~cm}^{2}$", "$60 \\mathrm{~cm}^{2}$", "$64 \\mathrm{~cm}^{2}$", "I don't know" ]

images/1024.jpg

B

null

4

solid geometry

B

1029

The first row shows 11 cards, each with two letters. The second row shows rearangement of the cards. Which of the following could appear on the bottom line of the second row? <image1>

[ "ANJAMKILIOR", "RLIIMKOJNAA", "JANAMKILIRO", "RAONJMILIKA", "ANMAIKOLIRJ", "I don't know" ]

images/1029.jpg

E

null

4

algebra

E

1033

There are six identical circles in the picture. The circles touch the sides of a large rectangle and one another as well. The vertices of the small rectangle lie in the centres of the four circles, as illustrated. The perimeter of the small rectangle is $60 \mathrm{~cm}$. What is the perimeter of the large rectangle? <...

[ "$160 \\mathrm{~cm}$", "$140 \\mathrm{~cm}$", "$120 \\mathrm{~cm}$", "$100 \\mathrm{~cm}$", "$80 \\mathrm{~cm}$", "I don't know" ]

images/1033.jpg

D

null

2

metric geometry - length

D

1034

$A B C$ and $C D E$ are equal equilateral triangles. If $\angle A C D=80^{\circ}$, what is $\angle A B D$? <image1>

[ "$25^{\\circ}$", "$30^{\\circ}$", "$35^{\\circ}$", "$40^{\\circ}$", "$45^{\\circ}$", "I don't know" ]

images/1034.jpg

D

null

5

metric geometry - angle

D

1036

Which of the following objects can be obtained by rotating in space the grey object? <image1> <image2>

[ "W and Y", "X and Z", "Only Y", "None of these", "W, X ir Y", "I don't know" ]

images/1036.jpg

A

null

4

solid geometry

A

1038

In the picture there is a square tile with two fourths of a circle. The radius of every fourth is half the side of the tile and its length equals $5 \mathrm{dm}$. We form a large square from 16 such tiles and try to get the longest unbroken curve consisting of the fourths. How long can this continuous curve be at most?...

[ "$75 \\mathrm{dm}$", "$100 \\mathrm{dm}$", "$105 \\mathrm{dm}$", "$110 \\mathrm{dm}$", "$80 \\mathrm{dm}$", "I don't know" ]

images/1038.jpg

D

null

4

combinatorial geometry

D

1041

Three lines intersect at one point. Two angles are given in the figure. How many degrees does the grey angle have? <image1>

[ "$52^{\\circ}$", "$53^{\\circ}$", "$54^{\\circ}$", "$55^{\\circ}$", "$56^{\\circ}$", "I don't know" ]

images/1041.jpg

A

null

5

metric geometry - angle

A

1043

Four tangent congruent circles of radius $6 \mathrm{~cm}$ are inscribed in a rectangle. <image1> If $P$ is a vertex and $Q$ and $R$ are the points of tangency, what is the area of triangle $P Q R$?

[ "$27 \\mathrm{~cm}^{2}$", "$45 \\mathrm{~cm}^{2}$", "$54 \\mathrm{~cm}^{2}$", "$108 \\mathrm{~cm}^{2}$", "$180 \\mathrm{~cm}^{2}$", "I don't know" ]

images/1043.jpg

D

null

3

metric geometry - area

D

1044

In an isosceles triangle $A B C(A B=A C)$, the bisector $C D$ of the angle $C$ is equal to the base $B C$. Then the angle $C D A$ is equal to <image1>

[ "$90^{\\circ}$", "$100^{\\circ}$", "$108^{\\circ}$", "$120^{\\circ}$", "Impossible to determine", "I don't know" ]

images/1044.jpg

C

null

5

metric geometry - angle

C

1047

The star shown in the picture is made by fitting together 12 congruent equilateral triangles. The perimeter of the star is $36 \mathrm{~cm}$. What is the perimeter of the grey hexagon? <image1>

[ "$6 \\mathrm{~cm}$", "$12 \\mathrm{~cm}$", "$18 \\mathrm{~cm}$", "$24 \\mathrm{~cm}$", "$30 \\mathrm{~cm}$", "I don't know" ]

images/1047.jpg

C

null

4

combinatorial geometry

C

1048

In the picture the large square has an area of 1. What is the area of the small black square? <image1>

[ "$\\frac{1}{100}$", "$\\frac{1}{300}$", "$\\frac{1}{600}$", "$\\frac{1}{900}$", "$\\frac{1}{1000}$", "I don't know" ]

images/1048.jpg

D

null

5

arithmetic

D

1049

In the diagram QSR is a straight line. $\angle \mathrm{QPS}=12^{\circ}$ and $\mathrm{PQ}=\mathrm{PS}=\mathrm{RS}$. How big is $\angle \mathrm{QPR}$? <image1>

[ "$36^{\\circ}$", "$42^{\\circ}$", "$54^{\\circ}$", "$60^{\\circ}$", "$84^{\\circ}$", "I don't know" ]

images/1049.jpg

C

null

5

metric geometry - angle

C

1050

Which of the following is made using more than one piece of string? <image1>

[ "I, III, IV and V", "I, III and V", "III, IV and V", "all", "None of these answers", "I don't know" ]

images/1050.jpg

B

null

3

topology

B

1052

What fraction of the largest square is grey? <image1>

[ "$\\frac{1}{4}$", "$\\frac{1}{5}$", "$\\frac{2}{5}$", "$\\frac{3}{8}$", "$\\frac{1}{3}$", "I don't know" ]

images/1052.jpg

A

null

3

metric geometry - area

A

1054

We want to paint each square in the grid with the colours P, Q, R and S, so that neighbouring squares always have different colours. (Squares which share the same corner point also count as neighbouring.) Some of the squares are already painted. In which colour(s) could the grey square be painted? <image1>

[ "only Q", "only R", "only S", "either R or S", "it is not possible.", "I don't know" ]

images/1054.jpg

D

null

3

graph theory

D

1055

The diagram opposite shows a regular nonagon. What is the size of the angle marked $\mathrm{X}$? <image1>

[ "$40^{\\circ}$", "$45^{\\circ}$", "$50^{\\circ}$", "$55^{\\circ}$", "$60^{\\circ}$", "I don't know" ]

images/1055.jpg

E

null

5

metric geometry - angle

E

1058

The fractions $\frac{1}{3}$ und $\frac{1}{5}$ are shown on the number line. In which position should $\frac{1}{4}$ be shown? <image1>

[ "a", "b", "c", "d", "e", "I don't know" ]

images/1058.jpg

A

null

4

algebra

A

1059

A cube is cut in three directions as shown, to produce eight cuboids (each cut is parallel to one of the faces of the cube). What is the ratio of the total surface area of the eight cuboids to the surface area of the original cube? <image1>

[ "1:1", "4:3", "3:2", "2:1", "4:1", "I don't know" ]

images/1059.jpg

D

null

4

solid geometry

D

1061

The perimeter of the figure pictured on the right is...... <image1>

[ "$3 a+4 b$", "$3 a+8 b$", "$6 a+4 b$", "$6 a+6 b$", "$6 a+8 b$", "I don't know" ]

images/1061.jpg

E

null

2

metric geometry - length

E

1062

Martina draws the six cornerpoints of a regular hexagon and then connects some of them to obtain a geometric figure. Which of the following figures cannot be generated? <image1>

[ "trapezium", "right angled triangle", "square", "kite", "obtuse triangle", "I don't know" ]

images/1062.jpg

C

null

4

combinatorial geometry

C

1064

In the quadrilateral $\mathrm{ABCD}, \mathrm{AD}=\mathrm{BC}, \angle \mathrm{DAC}=50^{\circ}$, $\angle \mathrm{DCA}=65^{\circ}$ and $\angle \mathrm{ACB}=70^{\circ}$. How big is $\angle \mathrm{ABC}$? <image1>

[ "$50^{\\circ}$", "$55^{\\circ}$", "$60^{\\circ}$", "$65^{\\circ}$", "It is not clear.", "I don't know" ]

images/1064.jpg

B

null

5

metric geometry - angle

B

1065

Andrea wraps a band around a piece of wood. She then turns the wood around as pictured. What does the wood now look like? <image1> <image2>

[ "A", "B", "C", "D", "E", "I don't know" ]

images/1065.jpg

B

null

3

transformation geometry

B