Yuting6/geoqa-r1v-8k-rotated huggingface dataset:
Problem: <image>Question: 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>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: E
Problem: <image>Question: Which of the following geometrical figures does not appear in the big picture?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: D
Problem: <image>Question: Laura wants to colour in exactly one $2 \times 2$ square <image1> in the figure given <image2>. How many ways are there for her to do that?
Answer: 8
Problem: <image>Question: On each of the three separate pieces of paper there is a three-digit number. The sum of the three numbers is 826. What is the sum of the two hidden digits?
<image1>
Answer: 9
Problem: <image>Question: Pia has a folding yardstick consisting of 10 equally long pieces. Which of the following figures can she not make?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: A
Problem: <image>Question: Which of the five squares has the biggest proportion of black area?
<image1>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: B
Problem: <image>Question: 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?
Choices:
A. $9 \mathrm{~cm}$
B. $10 \mathrm{~cm}$
C. $11 \mathrm{~cm}$
D. $12 \mathrm{~cm}$
E. $14 \mathrm{~cm}$
Answer: C
Problem: <image>Question: Bridget folds a square piece of paper twice and subsequently cuts it along the two lines as shown in the picture.
<image1>
How many pieces of paper does she obtain this way?
Answer: 9
Problem: <image>Question: 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>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: D
Problem: <image>Question: A natural number greater than 0 is written on each side of the die shown. All products of opposite numbers are of the same value. What is the smallest possible sum of all 6 numbers?
<image1>
Answer: 41
Problem: <image>Question: 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>
Choices:
A. $100 \mathrm{~g}$
B. $99 \mathrm{~g}$
C. $96 \mathrm{~g}$
D. $94 \mathrm{~g}$
E. $90 \mathrm{~g}$
Answer: E
Problem: <image>Question: Benjamin writes a number into the first circle. He then carries out the calculations as instructed and each time writes down the results in the respective circles. How many of the six numbers are divisible by 3?
<image1>
Answer: 2
Problem: <image>Question: The cardboard is folded up into a $2 \times 1 \times 1$ box. Which of the pictures does not show the box?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: B
Problem: <image>Question: Jette and Willi throw balls at two identically built pyramids each made up of 15 tins. Jette hits 6 tins and gets 25 points. Willi hits 4 tins. How many points does Willi get?
<image1>
Answer: 26
Problem: <image>Question: Which tile below completes the wall next to it?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: E
Problem: <image>Question: Amira is traveling from Atown to Betown and passes by two indicative signs along the road. One of them has a hidden number. What is this number?
<image1>
Answer: 7
Problem: <image>Question: The board beside is formed by little white and dark squares. After a ninety-degree turn, how can this board appear?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: D
Problem: <image>Question: 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>
Choices:
A. 1,30
B. 1,35
C. 1,40
D. 1,55
E. 1,75
Answer: C
Problem: <image>Question: Cynthia paints each region of the figure in a single color: red, blue or yellow. She paints the regions that touch each other with different colors. In how many different ways can she color the figure?
<image1>
Answer: 6
Problem: <image>Question: Two little mice, one white and one dark, leave, at the same time, towards the cheese, through different paths, as indicated in the picture, in which the little squares are equal. The two arrive at the same time to the cheese. If the dark mouse runs 4.5 meters per second, how many meters per second does the white mouse run?
<image1>
Answer: 1.5
Problem: <image>Question: The circles of the figure should be numbered from 0 to 10 , each with a different number. The five sums of the three numbers written on each diameter must be odd numbers. If one of these sums is the smallest possible, what will be the largest possible value of one of the remaining sums?
<image1>
Answer: 21
Problem: <image>Question: 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?
Choices:
A. 2h 48m
B. 2h 59m
C. 3h 39m
D. 3h 41m
E. 3h 49m
Answer: D
Problem: <image>Question: 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>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: A
Problem: <image>Question: 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>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: A
Problem: <image>Question: 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>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: B
Problem: <image>Question: 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>
Choices:
A. (A)
B. (B)
C. (C)
D. (D)
E. (E)
Answer: E
Problem: <image>Question: Beatriz has five sisters with ages of 2, 3, 5, 8, 10 and 17. Beatriz writes these ages in the circles of the opposite diagram, so that the sum of the ages in the four corners of the square is equal to the sum of the ages in the four circles aligned horizontally. What is this sum?
<image1>
Answer: 32
Problem: <image>Question: 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>
Choices:
A. (A)
B. (B)
C. (C)
D. (D)
E. (E)
Answer: A
Problem: <image>Question: Inside the gray square there are three white squares and the numbers inside them indicate their areas. The white squares have sides parallel to the sides of the gray square. If the area of the gray square is 81, what is the area of the gray area not covered by the white squares?
<image1>
Answer: 52
Problem: <image>Question: John made a construction with wooden cubes of the same size, with the three views shown beside, using as many cubes as possible. Ana, John's sister, wants to remove all the cubes she can, without modifying these three views. At most, how many cubes can she remove?
front:
<image1>
right side:
<image2>
above:
<image3>
Answer: 12
Problem: <image>Question: A panel is composed of 4 circles. When Lucy touches a circle, this circle and the others that touch this circle change their color from white to black or from black to white, as shown in the picture. Starting with all white circles, at least how many circles must Lucy touch, one after the other, so that all circles turn black?
<image1>
Answer: 4
Problem: <image>Question: Which set of weights below balances the third scale, in the picture beside?
<image1>
<image2>
Choices:
A. (A)
B. (B)
C. (C)
D. (D)
E. (E)
Answer: D
Problem: <image>Question: 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 same, which of the following combinations is possible?
<image1>
Choices:
A. Chocolat and chocolate gum.
B. Mango and cherry.
C. Lemmon and wafer.
D. Mango and wafer.
E. Lemmon and cherry.
Answer: E
Problem: <image>Question: Dirce built the sculpture on the side by gluing cubic boxes of half a meter on the side. Then she painted the sculpture minus the support base, with a special paint sold in cans. Each can allow to paint 4 square meters of surface. How many cans of paint did she have to buy?
<image1>
Answer: 4
Problem: <image>Question: 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 numbers are in ascending order, starting with the number 1 at the top, after the folds are made above. On the open sheet, indicated at the side, which numbers should she write in place of $a, b$ and $c$?
<image1>
<image2>
Choices:
A. $a=9, b=5, c=3$
B. $a=4, b=6, c=8$
C. $a=7, b=5, c=3$
D. $a=3, b=5, c=7$
E. $a=6, b=4, c=7$
Answer: C
Problem: <image>Question: 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 to complete his route?
<image1>
Choices:
A. North.
B. East.
C. South.
D. West.
E. There is more than one possible choice
Answer: C
Problem: <image>Question: Which of the following solid shapes can be made with these 6 bricks?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: D
Problem: <image>Question: In how many places in the picture are two children holding each other with their left hands?
<image1>
Answer: 1
Problem: <image>Question: 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>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: E
Problem: <image>Question: 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>
Choices:
A. K
B. E
C. N
D. G
E. U
Answer: D
Problem: <image>Question: When the 5 pieces <image1> are fitted together correctly, the result is a rectangle with a calculation written on it. What is the answer to this calculation?
Answer: 32
Problem: <image>Question: A measuring tape is wound around a cylinder. What number should be at the place shown by the question mark?
<image1>
Answer: 69
Problem: <image>Question: 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>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: B
Problem: <image>Question: 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>
Choices:
A. only P
B. only Q
C. only R
D. only P or Q
E. any of P, Q or R
Answer: E
Problem: <image>Question: 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>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: D
Problem: <image>Question: 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 $13 \mathrm{~km}$ long. Also, A tour from the Zoo to the Park and the Port and back to the Zoo is $15 \mathrm{~km}$ long. How long is the shortest tour from A to B to $C$ and back to $A$?
<image1>
Choices:
A. $18 \mathrm{~km}$
B. $20 \mathrm{~km}$
C. $25 \mathrm{~km}$
D. $35 \mathrm{~km}$
E. $50 \mathrm{~km}$
Answer: B
Problem: <image>Question: 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>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: D
Problem: <image>Question: The diagram shows 3 hexagons with numbers at their vertices, but some numbers are invisible. The sum of the 6 numbers around each hexagon is 30. What is the number on the vertex marked with a question mark?
<image1>
Answer: 4
Problem: <image>Question: 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>
Choices:
A. $7 \mathrm{~cm}$
B. $7.5 \mathrm{~cm}$
C. $8 \mathrm{~cm}$
D. $8.2 \mathrm{~cm}$
E. $8.5 \mathrm{~cm}$
Answer: C
Problem: <image>Question: 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>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: A
Problem: <image>Question: 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>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: E
Problem: <image>Question: 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 same instant that a train starts from $Y$, without them colliding during the trip. Which of the following figures represents the line?
<image1>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: B
Problem: <image>Question: Maurice asked the canteen chef for the recipe for his pancakes. Maurice has 6 eggs, 400g flour, 0.5 liters of milk and 200g butter. What is the largest number of pancakes he can make using this recipe?
<image1>
Answer: 8
Problem: <image>Question: 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>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: A
Problem: <image>Question: What is the smallest number of shaded squares that can be added to the diagram to create a design, including the grid, with 4 axes of symmetry?
<image1>
Answer: 21
Problem: <image>Question: 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?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: C
Problem: <image>Question: Each shelf holds a total of 64 deciliters of apple juice. The bottles have three different sizes: large, medium and small. How many deciliters of apple juice does a medium bottle contain?
<image1>
Answer: 10
Problem: <image>Question: 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 used to form this rectangle?
<image2>
<image3>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: E
Problem: <image>Question: 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>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: E
Problem: <image>Question: Eva paddles around five buoys with her boat (see diagram). Which of the buoys does she paddle around in an anti-clockwise direction?
<image1>
Choices:
A. 1 and 4
B. 2, 3 and 5
C. 2 and 3
D. 1,4 and 5
E. 1 and 3
Answer: E
Problem: <image>Question: 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> ?
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: B
Problem: <image>Question: 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?
<image5>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: D
Problem: <image>Question: All vehicles in the garage can only drive forwards or backwards. The black car wants to leave the garage (see diagram). What is the minimum number of grey vehicles that need to move at least a little bit so that this is possible?
<image1>
Answer: 4
Problem: <image>Question: How much does this Ferris wheel need to turn so that a white gondola is on top for
the first time?
<image1>
Choices:
A. $\frac{1}{2}$ turn
B. $\frac{1}{3}$ turn
C. $\frac{1}{6}$ turn
D. $\frac{1}{12}$ turn
E. $\frac{5}{6}$ turn
Answer: D
Problem: <image>Question: The sides of the square $A B C D$ are $10 \mathrm{~cm}$ long. What is the total area of the shaded part?
<image1>
Choices:
A. $40 \mathrm{~cm}^{2}$
B. $45 \mathrm{~cm}^{2}$
C. $50 \mathrm{~cm}^{2}$
D. $55 \mathrm{~cm}^{2}$
E. $60 \mathrm{~cm}^{2}$
Answer: C
Problem: <image>Question: 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>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: C
Problem: <image>Question: Marc builds the number 2022 as seen in the picture by glueing together 66 cubes of the same size. Afterwards he paints the entire surface of his work. On how many of the 66 cubes has Marc painted exactly four faces?
<image1>
Answer: 60
Problem: <image>Question: 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>
Choices:
A. $25 \mathrm{~cm}$
B. $50 \mathrm{~cm}$
C. $75 \mathrm{~cm}$
D. $1 \mathrm{~m}$
E. $1.25 \mathrm{~m}$
Answer: D
Problem: <image>Question: 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>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: A
Problem: <image>Question: Four circles are always connected by a line to form chains of four in a drawing. The numbers 1, 2, 3 and 4 appear in each row, each column and each chain of four.
Which number is in the circle with the question mark?
<image1>
Answer: 2
Problem: <image>Question: 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>
Choices:
A. $22 \mathrm{~cm}$
B. $24 \mathrm{~cm}$
C. $28 \mathrm{~cm}$
D. $34 \mathrm{~cm}$
E. $40 \mathrm{~cm}$
Answer: D
Problem: <image>Question: 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>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: C
Problem: <image>Question: Werner inserts numbers in various ways into the empty squares <image1> in such a way that the calculation is correct. He always uses four of the numbers 2,3, 4, 5 or 6 where in each calculation each number is only allowed to appear once. How many of the five numbers can Werner insert into the grey square?
Answer: 5
Problem: <image>Question: A building is made up of cubes of the same size. The three pictures show it from above (von oben), from the front (von vorne) and from the right (von rechts). What is the maximum number of cubes used to make this building?
<image1>
Answer: 19
Problem: <image>Question: Each animal in the picture on the right represents a natural number greater than zero. Different animals represent a different numbers. The sum of the two numbers of each column is written underneath each column. What is the maximum value the sum of the four numbers in the upper row can have?
<image1>
Answer: 20
Problem: <image>Question: Kai has to insert the numbers $3,4,5,6$ and 7 into the five circles of the diagram on the right in the following way: The product of the three numbers in the vertices of each triangle has to be equal to the number stated within the triangle. How big is the sum of the numbers in the vertices of the triangle with the number 168?
<image1>
Answer: 17
Problem: <image>Question: Matchsticks are arranged to form numbers as shown. To form the number 15 one needs 7 matchsticks. To form the number 8 one needs the same amount. What is the biggest number that one can build using 7 matchsticks? <image1>
Answer: 711
Problem: <image>Question: Which of the shapes cannot be split into two triangles using a single straight line?
<image1>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: A
Problem: <image>Question: Nine steps of a staircase arranged in a cylindrical order starting at the bottom and leading all the way to the top can be seen. All steps are equally high. How many steps cannot be seen? <image1>
Answer: 12
Problem: <image>Question: Anna has five discs of different sizes. She wants to use 4 of them to build a tower. <image1> She always has to place a smaller one on top of a bigger one. How many ways are there for Anna to build the tower?
Answer: 5
Problem: <image>Question: 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?
Choices:
A. M, N, Q, P
B. N, M, P, Q
C. N, Q, M, P
D. N, M, Q, P
E. $Q, N, M, P$
Answer: D
Problem: <image>Question: Alice has four jigsaw pieces. <image1> Which two can be fitted together to form a hexagon?
Choices:
A. 1 and 2
B. 1 and 3
C. 2 and 3
D. 2 and 4
E. 1 and 4
Answer: B
Problem: <image>Question: 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>
Choices:
A. 4, 6 and 12
B. 1, 5 and 10
C. 2, 4 and 9
D. 3, 6 and 9
E. 5, 7 and 12
Answer: A
Problem: <image>Question: Jan sticks these three pieces of paper <image1> Which picture can he not obtain?
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: C