Yuting6/geoqa-r1v-8k-rotated huggingface dataset:
Problem: <image>Question: Nathalie wanted to build a large cube out of lots of small cubes. How many cubes are missing from the picture on the right that would be needed to build the large cube on the left?
<image1>
Answer: 7
Problem: <image>Question: How far must Maria walk to reach her friend Bianca?
<image1>
Choices:
A. $300 \mathrm{~m}$
B. $400 \mathrm{~m}$
C. $800 \mathrm{~m}$
D. $1 \mathrm{~km}$
E. $700 \mathrm{~m}$
Answer: C
Problem: <image>Question: Nick can turn right but not left on his bicycle. What is the least number of right turns he must make in order to get from $A$ to $B$?
<image1>
Answer: 4
Problem: <image>Question: Anne has a few grey tiles like the one in the picture.
<image1>
What is the maximum number of these tiles that she can place on the $5 \times 4$ rectangle without any overlaps?
<image2>
Answer: 4
Problem: <image>Question: Maria drew the following figures on square sheets of paper.
<image1>
How many of these figures have the same perimeter as the square sheet of paper itself?
Answer: 4
Problem: <image>Question: Patricia drives one afternoon at a constant speed to her friend. She looks at her watch as she leaves and when she arrives.
<image1>
In which position will the minute hand be when she has completed one third of her journey?
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: D
Problem: <image>Question: Johann stacks $1 \times 1$ cubes on the squares of a $4 \times 4$ grid. The diagram on the right shows how many cubes were piled on top of each other on each square of the grid. What will Johann see if he looks from behind (hinten) at the tower?
<image1>
<image2>
Choices:
A. (A)
B. (B)
C. (C)
D. (D)
E. (E)
Answer: C
Problem: <image>Question: A $1 \times 1 \times 1$ cube is cut out of each corner of a $3 \times 3 \times 3$ cube. The picture shows the result after the first cube is cut out. How many faces will the final shape have?
<image1>
Answer: 30
Problem: <image>Question: Which of the figures below will cover the most dots when laid on the square shown on the right.
<image1>
<image2>
Choices:
A. (A)
B. (B)
C. (C)
D. (D)
E. (E)
Answer: C
Problem: <image>Question: Numbers are written in the $4 \times 4$ grid: any two numbers in neighbouring squares should have a difference of 1 , that is squares that share an edge. The number 3 is already given. The number 9 will be used somewhere in the grid. How many different numbers will have been used once the grid is filled in completely?
<image1>
Answer: 7
Problem: <image>Question: Two buttons with smiling faces and two buttons with sad faces are in a row as shown in the picture. When you press a button the face changes, and so do the faces of the neighbouring buttons. What is the minimum number of button presses needed so that only smiling faces can be seen?
<image1>
Answer: 3
Problem: <image>Question: From an old model train set there are only identical pieces of track to use. Matthias puts 8 such pieces in a circle (picture on the left). Martin begins his track with 2 pieces as shown in the picture on the right. He also wants to build a closed track and use the smallest number of pieces possible. How many pieces will his track use?
<image1>
Answer: 12
Problem: <image>Question: Arno lays out the word KANGAROO using 8 cards. However, some cards are turned.
<image1>
By turning it twice the letter $\mathrm{K}$ can be corrected, letter $\mathrm{A}$ can be corrected by turning it once (see drawing). How often does he have to turn so that the word KANGAROO can be read correctly?
<image2>
Answer: 6
Problem: <image>Question: A white and a grey ring are interlinked with one another. Peter sees the two rings from the front as they are seen in the diagram on the right. Paul sees the rings from the back. What does he see?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: D
Problem: <image>Question: In the addition sum to the right, three digits have been replaced with stars. How big is the sum of the three missing digits?
<image1>
Answer: 0
Problem: <image>Question: A square with perimeter $48 \mathrm{~cm}$ is cut into two equally big pieces with one cut. They are fitted together to make a rectangle as shown in the diagram. How big is the perimeter of that rectangle?
<image1>
Choices:
A. $24 \mathrm{~cm}$
B. $30 \mathrm{~cm}$
C. $48 \mathrm{~cm}$
D. $60 \mathrm{~cm}$
E. $72 \mathrm{~cm}$
Answer: D
Problem: <image>Question: Grey and white pearls are threaded on a piece of string.
<image1>
Monika wants to have 5 grey pearls. However, she can only pull off pearls from the end of the string. Therefore she has to pull off some white pearls as well. What is the minimum number of white pearls she has to pull off, to get 5 grey pearls?
Answer: 3
Problem: <image>Question: Which square has to replace the question mark so that the white area and the black area are equally big?
<image1>
<image2>
Choices:
A. (A)
B. (B)
C. (C)
D. (D)
E. (E)
Answer: B
Problem: <image>Question: The kangaroos $A, B, C, D$ and $E$ sit in this order in a clockwise direction around a round table. After a bell sounds all but one kangaroo change seats with a neighbour. Afterwards they sit in the following order in a clockwise direction: A, E, B, D, C. Which kangaroo did not change places?
<image1>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: B
Problem: <image>Question: A square can be made out of four of the given pieces. Which piece will not be used?
<image1>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: B
Problem: <image>Question: The $3 \times 3 \times 3$ cube consists of 27 small cubes.
<image1>
Some of the small cubes are removed. If you now look at the cube from the right, from above and from the front, you see the following: <image2> How many little cubes were removed?
Answer: 7
Problem: <image>Question: Daniela fills a $3 \times 3$ table using the digits 1 to 9 so that each field contains only one digit. She has already placed the digits 1, 2, 3 and 4 in the table as shown in the diagram. Two numbers count as "adjacent" if the fields which they fill have one common side. When she has finished filling the table she realised: the sum of the numbers adjacent to 5 is 9 . How big is the sum of the numbers adjacent to 6?
<image1>
Answer: 29
Problem: <image>Question: In which shape is exactly one half coloured grey?
<image1>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: B
Problem: <image>Question: The word KANGAROO is written on the top side of my umbrella. Which of the following pictures does not show my umbrella?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: C
Problem: <image>Question: Sam paints the 9 small squares in the shape either white, grey or black. What is the minimum number he must paint over so that no two squares sharing a side have the same colour?
<image1>
Answer: 2
Problem: <image>Question: Each square in the shape has an area of $4 \mathrm{~cm}^{2}$. How long is the thick line?
<image1>
Choices:
A. $16 \mathrm{~cm}$
B. $18 \mathrm{~cm}$
C. $20 \mathrm{~cm}$
D. $21 \mathrm{~cm}$
E. $23 \mathrm{~cm}$
Answer: B
Problem: <image>Question: <image1>
How much does Dita weigh?
Choices:
A. $2 \mathrm{~kg}$
B. $3 \mathrm{~kg}$
C. $4 \mathrm{~kg}$
D. $5 \mathrm{~kg}$
E. $6 \mathrm{~kg}$
Answer: D
Problem: <image>Question: Peter looks at the picture hanging on the wall in more detail through a magnifying glass. Which section can he not see?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: E
Problem: <image>Question: Each plant in Johns garden has exactly 5 leaves or exactly 2 leaves and a flower. In total the plants have 6 flowers and 32 leaves. How many plants are growing in the garden?
<image1>
Answer: 10
Problem: <image>Question: Andrea has 4 equally long strips of paper. When she glues two together with an overlap of $10 \mathrm{~cm}$, she gets a strip $50 \mathrm{~cm}$ long.
<image1>
With the other two she wants to make a $56 \mathrm{~cm}$ long strip. How long must the overlap be?
<image2>
Choices:
A. $4 \mathrm{~cm}$
B. $6 \mathrm{~cm}$
C. $8 \mathrm{~cm}$
D. $10 \mathrm{~cm}$
E. $12 \mathrm{~cm}$
Answer: A
Problem: <image>Question: Thomas has made the following shape with 6 squares of side length 1. What is the perimeter of the shape?
<image1>
Answer: 12
Problem: <image>Question: A rectangle is formed from 4 equally sized smaller rectangles. The shorter side is $10 \mathrm{~cm}$ long. How long is the longer side?
<image1>
Choices:
A. $40 \mathrm{~cm}$
B. $30 \mathrm{~cm}$
C. $20 \mathrm{~cm}$
D. $10 \mathrm{~cm}$
E. $5 \mathrm{~cm}$
Answer: C
Problem: <image>Question: Each of the 9 sides of the triangles in the picture will be coloured blue, green or red. Three of the sides are already coloured. Which colour can side $\mathrm{x}$ have, if the sides of each triangle must be coloured in three different colours?
<image1>
Choices:
A. only blue
B. only green
C. only red
D. Each of the three colours is possible.
E. The colouring described is not possible
Answer: C
Problem: <image>Question: For the game of Chess a new piece, the Kangaroo, has been invented. With each jump the kangaroo jumps either 3 squares vertically and 1 Horizontally, or 3 horizontally and 1 vertically, as pictured. What is the smallest number of jumps the kangaroo must make to move from its current position to position $\mathrm{A}$ ?
<image1>
Answer: 3
Problem: <image>Question: Nina wants to make a cube from the paper net. You can see there are 7 squares Instead of 6. Which square(s) can she remove from the net, so that the other 6 squares remain connected and from the newly formed net a cube can be made?
<image1>
Choices:
A. only 4
B. only 7
C. only 3 or 4
D. only 3 or 7
E. only 3,4 or 7
Answer: D
Problem: <image>Question: In how many ways can the three kangaroos be placed in three different squares so that no kangaroo has an immediate neighbour?
<image1>
Answer: 10
Problem: <image>Question: Maria writes a number on each face of the cube. Then, for each corner point of the cube, she adds the numbers on the faces which meet at that corner. (For corner B she adds the numbers on faces BCDA, BAEF and BFGC.) In this way she gets a total of 14 for corner C, 16 for corner D, and 24 for corner E. Which total, does she get for corner F?
<image1>
Answer: 22
Problem: <image>Question: Which of the following road signs has the most axes of symmetry?
<image1>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: C
Problem: <image>Question: $A 10 \mathrm{~cm}$ long piece if wire is folded so that every part is equally long (see diagram). The wire is then cut through in the two positions marked. How long are the three pieces created in this way?
<image1>
Choices:
A. $2 \mathrm{~cm}, 3 \mathrm{~cm}, 5 \mathrm{~cm}$
B. $2 \mathrm{~cm}, 2 \mathrm{~cm}, 6 \mathrm{~cm}$
C. $1 \mathrm{~cm}, 4 \mathrm{~cm}, 5 \mathrm{~cm}$
D. $1 \mathrm{~cm}, 3 \mathrm{~cm}, 6 \mathrm{~cm}$
E. $3 \mathrm{~cm}, 3 \mathrm{~cm}, 4 \mathrm{~cm}$
Answer: A
Problem: <image>Question: Lisa has mounted 7 postcards on her fridge door using 8 strong magnets (black dots). What is the maximum amount of magnets she can remove without any postcards falling on the floor?
<image1>
Answer: 4
Problem: <image>Question: Kathi draws a square with side length $10 \mathrm{~cm}$. Then she joins the midpoints of each side to form a smaller square. What is the area of the smaller square?
<image1>
Choices:
A. $10 \mathrm{~cm}^{2}$
B. $20 \mathrm{~cm}^{2}$
C. $25 \mathrm{~cm}^{2}$
D. $40 \mathrm{~cm}^{2}$
E. $50 \mathrm{~cm}^{2}$
Answer: E
Problem: <image>Question: Maria wants there to be a knife to the right of every plate and a fork to the left of it. In order to get the right order she always swaps one fork with one knife. What is the minimum number of swaps necessary?
<image1>
Answer: 2
Problem: <image>Question: Four girls are sleeping in a room with their heads on the grey pillows. Bea and Pia are sleeping on the left hand side of the room with their faces towards each other; Mary and Karen are on the right hand side with their backs towards each other. How many girls sleep with their right ear on the pillow?
<image1>
Answer: 2
Problem: <image>Question: The given net is folded along the dotted lines to form an open box. The box is placed on the table so that the opening is on the top. Which side is facing the table?
<image1>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: B
Problem: <image>Question: Robert has two equally big squares made of paper. He glues them together. Which of the following shapes can he not make?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: A
Problem: <image>Question: Five squirrels $A, B, C, D$ and $E$ are sitting on the points marked. The crosses indicate 6 nuts that they are collecting. The squirrels start to run at the same time with the same speed to the nearest nut in order to pick it up. As soon as a squirrel has picked up the first nut it immediately continues to run in order to get another nut. Which squirrel gets a second nut?
<image1>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: C
Problem: <image>Question: Bart sits at the hairdressers. In the mirror he sees a clock as shown in the diagram: What was the mirror image of the clock 10 minutes earlier?
<image1>
<image2>
Choices:
A. (A)
B. (B)
C. (C)
D. (D)
E. (E)
Answer: E
Problem: <image>Question: What is the maximum number of such pieces <image1> that can be cut from a 5 x 5 square?
<image2>
Answer: 6
Problem: <image>Question: The perimeter of the rectangle $A B C D$ is $30 \mathrm{~cm}$. Three more rectangles are added so that their centres are in the corners A, B and D and their sides are parallel to the rectangle (see diagram). The sum of the perimeters of these three rectangles is $20 \mathrm{~cm}$. What is the length of the boarder of the shape (thick black line)?
<image1>
Choices:
A. $50 \mathrm{~cm}$
B. $45 \mathrm{~cm}$
C. $40 \mathrm{~cm}$
D. $35 \mathrm{~cm}$
E. This cannot be calculated.
Answer: C
Problem: <image>Question: Clara forms one big triangle made up of identical little triangles. She has already put some triangles together (see diagram). What is the minimum number of little triangles she has to add?
<image1>
Answer: 9
Problem: <image>Question: Kirsten has written numbers into 5 of the 10 circles. She wants to write numbers into the remaining circles so that the sum of the three numbers along every side of the pentagon is always the same. Which number does she have to write into the circle marked
$X$?
<image1>
Answer: 13
Problem: <image>Question: Anna has four identical building blocks that each look like this: <image1> Which shape can she not form with them?
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: E
Problem: <image>Question: The 10 islands are connected by 12 bridges (see diagram). All bridges are open for traffic. What is the minimum number of bridges that need to be closed off, so that the traffic between $A$ and $B$ comes to a halt?
<image1>
Answer: 2
Problem: <image>Question: Jane, Kate and Lynn go for a walk. Jane walks at the very front, Kate in the middle and Lynn at the very back. Jane weighs $500 \mathrm{~kg}$ more than Kate and Kate weighs $1000 \mathrm{~kg}$ less than Lynn. Which of the following pictures shows Jane, Kate and Lynn in the right order?
<image1>
Choices:
A. (A)
B. (B)
C. (C)
D. (D)
E. (E)
Answer: A
Problem: <image>Question: Max colours in the squares of the grid, so that one third of all squares are blue and one half of all squares are yellow. The rest he colours in red. How many squares does he have to colour in red?
<image1>
Answer: 3
Problem: <image>Question: A rectangle is twice as long as wide. Which fraction of the rectangle is coloured in grey?
<image1>
Choices:
A. $\frac{1}{4}$
B. $\frac{3}{8}$
C. $\frac{3}{4}$
D. $\frac{1}{2}$
E. $\frac{3}{5}$
Answer: B
Problem: <image>Question: A furniture shop sells 3-seater, 2-seater and 1-seater sofas that each have an equally wide armrest on the left and the right hand side. Each seat is equally wide (see picture). Together with the armrests the 3-seater sofa is $220 \mathrm{~cm}$ and the 2-seater sofa $160 \mathrm{~cm}$ wide. How wide is the 1-seater sofa?
<image1>
Choices:
A. $60 \mathrm{~cm}$
B. $80 \mathrm{~cm}$
C. $90 \mathrm{~cm}$
D. $100 \mathrm{~cm}$
E. $120 \mathrm{~cm}$
Answer: D
Problem: <image>Question: Boris wants to increase his pocket money. To achieve this a fairy gives him three magic wands. He has to use every single one exactly once.
<image1>
In which order does he have to use the magic wands, in order to get the most money?
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: D
Problem: <image>Question: Raphael has three squares. The first one has side length $2 \mathrm{~cm}$, the second one has side length $4 \mathrm{~cm}$ and one corner is the centre of the first square. The third square has side length $6 \mathrm{~cm}$ and one corner is the centre of the second square. What is the total area of the figure shown?
<image1>
Choices:
A. $51 \mathrm{~cm}^{2}$
B. $32 \mathrm{~cm}^{2}$
C. $27 \mathrm{~cm}^{2}$
D. $16 \mathrm{~cm}^{2}$
E. $6 \mathrm{~cm}^{2}$
Answer: A
Problem: <image>Question: A big cube is made up of 9 identical building blocks. Each building block looks like this: <image1> Which big cube is possible?
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: A
Problem: <image>Question: The numbers $1,2,3,4$ and 5 have to be written into the five fields of this diagram according to the following rules: If one number is below another number, it has to be greater; if one number is to the right of another, it has to be greater. How many ways are there to place the numbers?
<image1>
Answer: 6
Problem: <image>Question: There are eight kangaroos in a row, as seen in the picture.
<image1>
Two kangaroos, that are standing next to each other and that are looking into each others eyes, are changing places by hopping past each other. This is carried out until no more jumps are possible. How often did a change of places occur?
Answer: 13
Problem: <image>Question: A square floor is made up of triangular and square tiles in grey and white. What is the smallest number of grey tiles that have to be swapped with white tiles, so that the floor looks the same from all four given viewing directions?
<image1>
Choices:
A. three triangles, one square
B. one triangle, three squares
C. one triangle, one square
D. three triangles, three squares
E. three triangles, two squares
Answer: C
Problem: <image>Question: Each one of the 5 keys locks exactly one padlock. Every letter on a padlock stands for exactly one digit, same letters mean same digits. Which digits are on the key with the question mark?
<image1>
Answer: 284
Problem: <image>Question: The first kangaroo is repeatedly mirrored along the dotted lines. Two reflections were already carried out. In which position is the kangaroo in the grey triangle?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: E
Problem: <image>Question: As seen in the diagram, three darts are thrown at nine fixed balloons. If a balloon is hit it will burst and the dart continues in the same direction it had beforehand. How many balloons will not be hit by a dart?
<image1>
Answer: 3
Problem: <image>Question: Peter places three building blocks on a table, as shown. What does he see when he is looking at them from above?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: C
Problem: <image>Question: If you hit the target board, you score points. The number of points depends on which one of the three areas you hit. Diana throws two darts, three times at the target board. On the first attempt she scores 14 points and on the second 16 points. How many points does she score on the third attempt?
<image1>
Answer: 18
Problem: <image>Question: A garden is split into equally sized square-shaped lots. A fast and snail crawls $1 \mathrm{~m}$ in one hour and the fast one crawls $2 \mathrm{~m}$ in one hour. In which position will the two snails meet for the first time?
<image1>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: B
Problem: <image>Question: A star consist of a square and four triangles. All sides of the triangles are equally long. The perimeter of the square is $36 \mathrm{~cm}$. What is the perimeter of the star?
<image1>
Choices:
A. $144 \mathrm{~cm}$
B. $120 \mathrm{~cm}$
C. $104 \mathrm{~cm}$
D. $90 \mathrm{~cm}$
E. $72 \mathrm{~cm}$
Answer: E
Problem: <image>Question: A big spot of ink covers most of a calendar page of a certain month. Which day of the week does the 25th day of that month fall on?
<image1>
Choices:
A. Monday
B. Wednesday
C. Thursday
D. Saturday
E. Sunday
Answer: D
Problem: <image>Question: A figure is made up of three squares. The side length of the smallest square is $6 \mathrm{~cm}$. How long is the side length of the biggest square?
<image1>
Choices:
A. $8 \mathrm{~cm}$
B. $10 \mathrm{~cm}$
C. $12 \mathrm{~cm}$
D. $14 \mathrm{~cm}$
E. $16 \mathrm{~cm}$
Answer: C
Problem: <image>Question: Alice subtracts one two-digit number from another two-digit number. Afterwards she paints over two digits in the calculation. How big is the sum of the two painted digits?
<image1>
Answer: 13
Problem: <image>Question: In the diagram the circles represent light bulbs which are connected to some other light bulbs. Initially all light bulbs are switched off. If you touch a light bulb then that light bulb and all directly adjacent light bulbs switch themselves on. What is the minimum number of light bulbs you have to touch in order to switch on all the light bulbs?
<image1>
Answer: 2
Problem: <image>Question: Four equally big squares are partially coloured in black. In which of the four squares is the total area of the black parts biggest?
<image1>
Choices:
A. A
B. B
C. C
D. D
E. The total area of the black parts is always equally big.
Answer: E
Problem: <image>Question: The four smudges hide four of the numbers $1,2,3,4,5$. The calculations along the two arrows are correct. Which number hides behind the smudge with the star?
<image1>
Answer: 5
Problem: <image>Question: The faces of a die are either white, grey or black. Opposite faces are always a different colour. Which of the following nets does not belong to such a die?
<image1>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: E
Problem: <image>Question: Emily wants to write a number into every free small triangle. The sum of the numbers in two triangles with a common side should always be the same. Two numbers are already given. How big is the sum of all numbers in the figure?
<image1>
Answer: 21
Problem: <image>Question: Instead of digits Hannes uses the letters A, B, C and D in a calculation. Different letters stand for different digits. Which digit does the letter B stand for?
<image1>
Answer: 0
Problem: <image>Question: Four ladybirds each sit on a different cell of a $4 \times 4$ grid. One is asleep and does not move. On a whistle the other three each move to an adjacent free cell. They can crawl up, down, to the right or to the left but are not allowed on any account to move back to the cell that they have just come from. Where could the ladybirds be after the fourth whistle?
Initial position:
<image1>
After the first whistle:
<image2>
After the second whistle:
<image3>
After the third whistle:
<image4>
<image5>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: A
Problem: <image>Question: The five balls weigh $30 \mathrm{~g}$, $50 \mathrm{~g}, 50 \mathrm{~g}, 50 \mathrm{~g}$ and $80 \mathrm{~g}$. Which of the balls weighs $30 \mathrm{~g}$ ?
<image1>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: C
Problem: <image>Question: The figure shown on the right consists of one square part and eight rectangular parts. Each part is $8 \mathrm{~cm}$ wide. Peter assembles all parts to form one long, $8 \mathrm{~cm}$ wide rectangle. How long is this rectangle?
<image1>
Choices:
A. $150 \mathrm{~cm}$
B. $168 \mathrm{~cm}$
C. $196 \mathrm{~cm}$
D. $200 \mathrm{~cm}$
E. $232 \mathrm{~cm}$
Answer: D
Problem: <image>Question: Carina has started to draw a cat. <image1> She then adds some eyes. Which picture could show her finished drawing?
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: B
Problem: <image>Question: 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>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: D
Problem: <image>Question: 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>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: C