Yuting6/geoqa-r1v-8k-rotated huggingface dataset:
Problem: <image>Question: A square piece of paper is folded twice so that the result is a square again. In this square one of the corners is cut off. Then the paper is folded out. Which sample below cannot be obtained in this way?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: E
Problem: <image>Question: We make a sequence of figures by dividing a square. The first four figures have 1, 4, 7 and 10 parts, respectively.
<image1>
How many parts will the fifth figure have?
Answer: 13
Problem: <image>Question: How many stars are inside the figure?
<image1>
Answer: 95
Problem: <image>Question: Rebecca has drawn a point on a sheet of paper. She now draws four straight lines that pass through this point. Into how many sections do these lines divide the paper?
<image1>
Answer: 8
Problem: <image>Question: The storm made a hole on the front side of the roof. There were 10 roof tiles in each of 7 rows. How many tiles are left on the front side of the roof?
<image1>
Answer: 57
Problem: <image>Question: Carol is playing with two equilateral triangular cards shown. She puts one card beside or on the top of a part of the other and both on a sheet of paper. Then she draws on the paper around them, following the contour. She cannot get only one of the shapes. Which one is it?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: E
Problem: <image>Question: Anna made the figure on the right out of five cubes. Which of the following figures (when seen from any direction) cannot she get from the figure on the right side if she is allowed to move exactly one cube?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: D
Problem: <image>Question: Which of the figures is shown most often in the sequence?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: D
Problem: <image>Question: We have a large number of blocks of $1 \mathrm{~cm} \times$ $2 \mathrm{~cm} \times 4 \mathrm{~cm}$. We will try to put as many of these blocks as possible into a box of $4 \mathrm{~cm} \times$ $4 \mathrm{~cm} \times 4 \mathrm{~cm}$ so that we were able to close the box with a lid. How many blocks fit in?
<image1>
Answer: 8
Problem: <image>Question: Jane shoots two arrows at the target. In the drawing we see that her score is 5. If both arrows hit the target, how many different scores can she obtain?
<image1>
Answer: 6
Problem: <image>Question: A garden of a square shape is divided into a pool (P), a flowerbed (F), a lawn (L) and a sandpit (S) (see the picture). The lawn and the flowerbed are of a square shape. The perimeter of the lawn is $20 \mathrm{~m}$, the perimeter of the flowerbed is $12 \mathrm{~m}$. What is the perimeter of the pool?
<image1>
Choices:
A. $10 \mathrm{~m}$
B. $12 \mathrm{~m}$
C. $14 \mathrm{~m}$
D. $16 \mathrm{~m}$
E. $18 \mathrm{~m}$
Answer: D
Problem: <image>Question: One of the cube faces is cut along its diagonals (see the fig.). Which two of the following nets are impossible?
<image1>
<image2>
Choices:
A. 1 and 3
B. 1 and 5
C. 3 and 4
D. 3 and 5
E. 2 and 4
Answer: D
Problem: <image>Question: Where is the Kangaroo?
<image1>
Choices:
A. In the circle and in the triangle but not in the square.
B. In the circle and in the square but not in the triangle.
C. In the triangle and in the square but not in the circle.
D. In the circle but in neither the square or the triangle.
E. In the square but in neither the circle or the triangle.
Answer: B
Problem: <image>Question: In the picture you see the number 930 . How many small squares must be changed so that the number becomes 806?
<image1>
<image2>
Answer: 6
Problem: <image>Question: In his garden Tony made a pathway using 10 paving stones. Each paver was $4 \mathrm{dm}$ wide and 6 dm long. He then drew a black line connecting the middle points of each paving stone. How long is the black line?
<image1>
Choices:
A. $24 \mathrm{dm}$
B. $40 \mathrm{dm}$
C. $46 \mathrm{dm}$
D. $50 \mathrm{dm}$
E. $56 \mathrm{dm}$
Answer: C
Problem: <image>Question: Peter shared a bar of chocolate. First he broke off a row with five pieces for his brother. Then he broke off a column with 7 pieces for his sister. How many pieces were there in the entire bar of chocolate?
<image1>
Answer: 40
Problem: <image>Question: Picture $X$ is paired with picture $Y$. Which of the following pictures is paired with picture $G$ ?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: E
Problem: <image>Question: Thomas has made a table out of small cubes. How many small cubes did he use?
<image1>
Answer: 32
Problem: <image>Question: Which of the following diagrams is impossible to make with the two dominos?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: E
Problem: <image>Question: Anna and Peter live in the same street. On one side of Anna's house there are 27 houses, and on the other side 13 houses. Peter lives in the house right in the middle of the street. How many houses are there between Anna's and Peter's houses?
<image1>
Answer: 6
Problem: <image>Question: Sylvia draws shapes made up of straight lines which are each $1 \mathrm{~cm}$ long. At the end of each line she continues in a right angle either to the left or right. At every turn she notes down either a $\vee$ or a $\wedge$ on a piece of paper. The same symbol always indicates a turn in the same direction. Today her notes show $\vee \wedge \wedge \wedge \vee \vee$. Which of the following shapes could she have drawn today if $A$ indicates her starting point?
<image1>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: E
Problem: <image>Question: In the picture on the right you see a map. In the middle a piece is missing. The cat should be able to reach the milk, and the mouse the cheese, but the cat and the mouse must not meet each other. What should the piece in the middle look like?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: E
Problem: <image>Question: Which square contains 3 quadrilaterals, 3 circles and 4 hearts?
<image1>
Choices:
A. A)
B. B)
C. C)
D. D)
E. E)
Answer: D
Problem: <image>Question: Six coins build a triangle (see picture). What is the smallest number of coins that must be moved to create the circle?
<image1>
Answer: 2
Problem: <image>Question: I have tiles that look like this...
<image1>
Which pattern can I not create with them?
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: B
Problem: <image>Question: Maria folds a square piece of paper in such a way that the kangaroos exactly overlap each other. Along how many of the lines shown is this possible?
<image1>
Answer: 2
Problem: <image>Question: A large cube is made from 64 small cubes. The 5 visible faces of the large cube are green, the bottom face is red. How many of the small cubes have 3 green faces?
<image1>
Answer: 4
Problem: <image>Question: Kamilla wrote down all of the numbers from 1-100 one after the other in a table with 5 columns. A part of the table is shown. Her brother cut out a piece of the table and erased some of the numbers. Which of the following could this piece have been?
<image1>
<image2>
Choices:
A. A)
B. B)
C. C)
D. D)
E. E)
Answer: C
Problem: <image>Question: lines are drawn on a piece of paper and some of the lines are given numbers. The paper is cut along some of these lines and then folded as shown in the picture. What is the total of the numbers on the lines that were cut?
<image1>
Answer: 20
Problem: <image>Question: Which stone should Mr Flintstone place on the right side of the scales, so that both sides weigh the same?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: C
Problem: <image>Question: A game is played on a board as shown in the picture. I move the counter from square to square according to the following rules. First, one square to the right, then one square up, then one square left, then one square down, and then once again one square right. Which picture shows where the counter can then be found?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: B
Problem: <image>Question: Maria describes one of these five shapes in the following way: "It is not a square. It is grey. It is either round or three sided." Which shape did she describe?
<image1>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: B
Problem: <image>Question: Which shape has the biggest area?
<image1>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: C
Problem: <image>Question: A page is folded along the thick line as shown. Which letter will not be covered by a grey square?
<image1>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: E
Problem: <image>Question: In each square of the maze there is a piece of cheese. Ronnie the mouse wants to enter and leave the maze as shown in the picture. He doesn't want to visit a square more than once, but would like to eat as much cheese as possible. What is the maximum number of pieces of cheese that he can eat?
<image1>
Answer: 37
Problem: <image>Question: How often in a day does a digital clock display four identical digits? The picture shows a digital clock that is displaying exactly two different digits.
<image1>
Choices:
A. 1 time
B. 24 times
C. 3 times
D. 5 times
E. 12 times
Answer: C
Problem: <image>Question: Four identical dice were put together to make a tower as shown. The sum of the numbers on opposite faces of each dice is always 7. What would the tower look like from behind?
<image1>
<image2>
Choices:
A. A)
B. B)
C. C)
D. D)
E. E)
Answer: C
Problem: <image>Question: You can place together the cards pictured, to make different three digit numbers, for instance 989 or 986. How many different three digit numbers can you make with these cards?
<image1>
Answer: 12
Problem: <image>Question: Andrea made the pattern in the picture out of several identical tiles. None of the tiles overlap each other. Which of the following tiles could she definitely not have used?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: D
Problem: <image>Question: The picture shows a Fortress made from cubes. How many cubes were used to make it?
<image1>
Answer: 56
Problem: <image>Question: Johannes wrote the numbers 6,7 and 8 in the circles as shown. He wants to write the numbers 1, 2, 3, 4 and 5 in the remaining circles so that the sum of the numbers along each side of the square is 13. What will be the sum of the numbers in the grey circles?
<image1>
Answer: 16
Problem: <image>Question: Sylvia draws patterns with hexagons as shown. If she carries on drawing in this way, how many hexagons will there be in the fifth pattern?
<image1>
Answer: 61
Problem: <image>Question: In which of the five pictures is the white area bigger than the grey area?
<image1>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: D
Problem: <image>Question: Father hangs towels on the washing as shown in the picture. For three towels he uses 4 clothes pegs. How many clothes pegs would he use for 5 towels?
<image1>
Answer: 6
Problem: <image>Question: Oli coloured in the following 8 fields in the grid: A2, B1, B2, B3, B4, C3, D3 and D4. Which is his grid?
<image1>
<image2>
Choices:
A. (A)
B. (B)
C. (C)
D. (D)
E. (E)
Answer: C
Problem: <image>Question: Mike and Jake play darts. Each of them throws three darts. Who won, and by how many points?
Mike: <image1>
Jake: <image2>
Choices:
A. Mike won. He had 3 points more.
B. Jake won. He had 4 points more.
C. Mike won. He had 2 points more.
D. Jake won. He had 2 points more.
E. Mike won. He had 4 points more.
Answer: E
Problem: <image>Question: A Wall was tiled alternately with grey and striped tiles. Some tiles have fallen from the wall. How many grey tiles have fallen off?
<image1>
Answer: 7
Problem: <image>Question: Anna has made two $L$ shapes out of 8 squares. How many of the following 4 shapes can she make with both $L$ shapes?
<image1>
<image2>
Answer: 4
Problem: <image>Question: You need 3 pieces to build this shape. Each piece is made out of 4 , equally sized cubes of the same colour. What is the shape of the white piece?
<image1>
<image2>
Choices:
A. (A)
B. (B)
C. (C)
D. (D)
E. (E)
Answer: D
Problem: <image>Question: A flee stands on the floor and wants to climb the 10 steps. He can either jump 3 steps upwards or jump 4 steps downwards. What is is the smallest number of jumps he must make?
<image1>
Answer: 8
Problem: <image>Question: Frank laid out his dominoes as shown in the picture. (Dominoes which touch must always have the same number of points). Before his brother George removed two dominoes there were 33 points altogether. How many points is the questionmark worth?
<image1>
Answer: 4
Problem: <image>Question: Grandma's watch has an hour, minute and second hand. We don't know which hand does which job, but we know that the watch tells the correct time. At 12:55:30 hours the watch looked as pictured. How will the watch look at 8:11:00 hours?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: E
Problem: <image>Question: How many more bricks does the right hand pyramid have than the left hand pyramid?
<image1>
Answer: 5
Problem: <image>Question: In which picture are there more black Kangaroos than white ones?
<image1>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: D
Problem: <image>Question: Anna has <image1>.
Barbara gave Eva <image2>.
Josef has a <image3>.
Bob has <image4>.
Who is Barbara?
<image5>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: D
Problem: <image>Question: Anna starts in the direction of the arrow. At each crossing she turns either right or left. At the first crossing she turns right, at the next left, then left again, then right, then left and left again. What will she find at the next crossing that she comes to?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: A
Problem: <image>Question: Nathalie wanted to build a large cube out of lots of small cubes, just like in picture 1. How many cubes are missing from picture 2 that would be needed to build the large cube?
<image1>
Answer: 7
Problem: <image>Question: The rectangular mirror has broken. Which piece is missing?
<image1>
<image2>
Choices:
A. (A)
B. (B)
C. (C)
D. (D)
E. (E)
Answer: B
Problem: <image>Question: How many triangles can be seen in the picture on the right? (Be careful! A triangle can be also be made by joining several smaller triangles together.)
<image1>
Answer: 10
Problem: <image>Question: Which of the following pieces can be joined to the one pictured so that a rectangle is formed?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: B
Problem: <image>Question: If I join the midpoints of the sides of the large triangle in the picture, a small triangle is formed. If I join the midpoints of the sides of this small triangle, a tiny triangle is formed. How many of these tiny triangles can fit into the largest triangle at the same time?
<image1>
Answer: 16
Problem: <image>Question: Baris has a few dominoes as shown in the picture. He wants to lay them in a line according to the rules of dominoes, that is that two dominoes can only be laid together if the neighbouring squares have the same number of dots in them. What is the biggest number of these dominoes that he can lay in a single line?
<image1>
Answer: 5
Problem: <image>Question: Peter has bought a rug that is $36 \mathrm{dm}$ wide and $60 \mathrm{dm}$ long. On the rug you can see squares that contain either a sun or a moon, as shown in the picture. As you can see there are exactly nine squares along the width of the rug. The total length of the rug cannot be seen. How many moons would you see, if you could see the entire rug?
<image1>
Answer: 67
Problem: <image>Question: Beatrice has a few grey tiles that all look exactly like the one pictured. At least how many of these tiles does she need in order to make a complete square?
<image1>
Answer: 4
Problem: <image>Question: Luisa draws a star. She cuts a piece out of the middle of the drawing. What does this piece look like?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: D
Problem: <image>Question: For which houses, were exactly the same building blocks used?
<image1>
Choices:
A. House 1 and 4
B. House 3 and 4
C. House 1, 4 and 5
D. House 3, 4 and 5
E. House 1, 2, 4 and 5
Answer: A
Problem: <image>Question: Christopher solved the sums next to the dots that you can see on the right, and got the answers 0 to 5 . He joined the dots in order. He started with the dot that had the answer 0 and finished with the dot that had the answer 5 . Which shape was he left with?
<image1>
<image2>
Choices:
A. (A)
B. (B)
C. (C)
D. (D)
E. (E)
Answer: A
Problem: <image>Question: Mr Hofer has drawn a picture of flowers on the inside of a display window (large picture). What do these flowers look like when you look at the picture from the outside?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: E
Problem: <image>Question: With which square do you have to swap the question mark, so that the white area and the black area are the same size?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: B
Problem: <image>Question: The solid in the diagram is made out of 8 identical cubes. What does the solid look like when viewed from above?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: C
Problem: <image>Question: Leo writes numbers in the multiplication pyramid. Explanation of the multiplication pyramid: By multiplying the numbers which are next to each other, the number directly above (in the middle) is calculated. Which number must Leo write in the grey field?
<image1>
Answer: 8
Problem: <image>Question: Katja throws darts at the target pictured on the right. If she does not hit the target she gets no points. She throws twice and adds her points. What can her total not be?
<image1>
Choices:
A. 60
B. 70
C. 80
D. 90
E. 100
Answer: D
Problem: <image>Question: Erwin has got the following paper pieces:
<image1>
With these four pieces he must exactly cover a special shape. In which drawing will he manage this, if the piece <image2> is placed as shown?
<image3>
Choices:
A. (A)
B. (B)
C. (C)
D. (D)
E. (E)
Answer: C
Problem: <image>Question: Gerhard has the same number of white, grey and black counters. He has thrown some of these circular pieces together onto a pile. All the pieces he has used for this, can be seen in the picture. He has however, got 5 counters left that will not stay on the pile. How many black counters did he have to begin with?
<image1>
Answer: 6
Problem: <image>Question: How many dots are in the picture?
<image1>
Answer: 181
Problem: <image>Question: Seven children stand in a circle. Nowhere are two boys found standing next to each other. Nowhere are three girls found standing next to each other. What is possible for the number of girls? The number of girls can...
<image1>
Choices:
A. ... only be 3.
B. ... be 3 or 4.
C. ... be 4 or 5.
D. ... only be 5.
E. ... only be 4.
Answer: C
Problem: <image>Question: Elisabeth sorts the following cards:
<image1>
With each move she is allowed to swap any two cards with each other. What is the smallest number of moves she needs in order to get the word KANGAROO.
Answer: 3
Problem: <image>Question: The number of black diamonds <image1> and white diamonds <image2> follow a fixed system. In the picture the first 3 levels are shown. Each level (from the $2^{\text{nd}}$ level) has one row more than the level before. For each level the following applies: In the last row both of the outermost diamonds are white, all other diamonds are black. How many black diamonds are there in level 6?
<image3>
Answer: 26
Problem: <image>Question: Heinzi the kangaroo has bought some toys. For this he gave 150 Kangoo-coins (KC) and received 20 kangoo-coins back. Just before leaving the shop he changed his mind, and exchanged one of the toys he had bought with another one. Therefore he received a further 5 kangoo-coins back from the shopkeeper. Which of the toys in the picture has Heinzi taken home with him?
<image1>
Choices:
A. Carriage and Aeroplane
B. Carriage and Bus
C. Carriage and Tram
D. Motorbike and Tram
E. Bus, Motorbike and Tram
Answer: A
Problem: <image>Question: In each box exactly one of the digits $0,1,2,3,4,5$ and 6 is to be written. Each digit will only be used once. Which digit has to be written in the grey box so that the sum is correct?
<image1>
Answer: 5
Problem: <image>Question: In the figure on the right a few of the small squares will be painted grey. In so doing no square <image1> that is made from four small grey squares must appear. At most how many of the squares in the figure can be painted grey?
<image2>
Answer: 21
Problem: <image>Question: Albin has put each of the digits from 1 to 9 in the fields of the table. In the diagram only 4 of these digits are visible. For the field containing the number 5, Albin noticed that the sum of the numbers in the neighbouring fields is 13. (neighbouring fields are fields which share a side). He noticed exactly the same for the field containing the digit 6 . Which digit had Albin written in the grey field?
<image1>
Answer: 8
Problem: <image>Question: <image1>
Answer: 15
Problem: <image>Question: Florian has 10 identical metal strips, each with the same amount of holes (picture above). He bolts these strips in pairs. That way he gets the 5 long strips in the picture below. Which of the long strips is the longest?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: A
Problem: <image>Question: In kangaroo land you pay with "Kangas". Lucy has a few Kangas in her purse. She buys a ball and pays 7 Kangas. How many Kangas does she have left over, after she has paid fort he ball?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: B
Problem: <image>Question: Which number is hidden behind the square?
<image1>
Answer: 6
Problem: <image>Question: The word Kangaroo is written on the top of my umbrella. Which of the 5 pictures shows my umbrella
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: A
Problem: <image>Question: 9 points, numbered 1 to 9 are marked on a circle. Point 1 is joined to point 3, 3 to 5. Continue the drawing, always joining to the next but one point along. Which drawing do you get if you keep going until you get back to point 1?
<image1>
<image2>
Choices:
A. (A)
B. (B)
C. (C)
D. (D)
E. (E)
Answer: E
Problem: <image>Question: In the diagram you can see a very ragged island. Some of the frogs are sitting in the water. How many are sitting on the island?
<image1>
Answer: 6
Problem: <image>Question: Julia folds the paper net pictured on the right, into a cube. Which number is on the face that is opposite to the face with the number 3?
<image1>
Answer: 6
Problem: <image>Question: Jack makes a cube from 27 small cubes. The small cubes are either grey or white as shown in the diagram. Two small cubes with the same colour are not allowed to be placed next to each other. How many small, white cubes has Jack used?
<image1>
Answer: 13
Problem: <image>Question: Peter rides his bike along a cycle path in a park. He starts at point $S$ and rides in the direction of the arrow. At the first crossing he turns right, then at the next left, and then again to the right and then again to left. Which crossing does he not reach?
<image1>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: D
Problem: <image>Question: Two of the 5 ladybirds in the picture are always friends with each other if the difference between their number of dots is exactly 1. Today every ladybird has sent an SMS to each of their friends. How many SMS messages were sent?
<image1>
Answer: 6
Problem: <image>Question: There are 10 balls, numbered 0 to 9 in a basket. John and George play a game. Each person is allowed to take three balls from the basket and calculate the total of the numbers on the balls. What is the biggest possible difference between the john and Georges totals?
<image1>
Answer: 21
Problem: <image>Question: Luca wants to cut the shape in figure 1 into equally sized small triangles (like those in figure 2). One of these triangles is already drawn on figure 1. How many of these triangles will he get?
<image1>
Answer: 15
Problem: <image>Question: Some of the small squares on each of the square transparencies have been coloured black. If you slide the three transparencies on top of each other, without lifting them from the table, a new pattern can be seen. What is the maximum number of black squares which could be seen in the new pattern?
<image1>
Answer: 8