Yuting6/geoqa-r1v-8k-rotated huggingface dataset:
Problem: <image>Question: The teacher wrote the numbers 1 to 8 on the board. Then he covered the numbers with triangles, squares and a circle. The sum of the numbers covered with the triangles equals the sum of the numbers covered with the squares and the number covered with the circle is a quarter of that sum. What is the sum of the numbers covered with the triangles and the circle?
<image1>
Answer: 20
Problem: <image>Question: Joana has several sheets of paper with the drawing of a parrot <image1>. She wants to paint only the head, tail and wing of the parrot, red, blue or green, and the head and tail may have the same color, but the wing may not have the same color as the head or tail. How many leaves can she paint, so that there are not two parrots painted the same way?
Answer: 12
Problem: <image>Question: The Kangaroo Hotel has 30 floors numbered from 1 to 30 and each floor has 20 rooms numbered from 1 to 20. The code to enter the room is formed by joining the floor number with the room number, in that order. But this code can be confusing, as shown in the picture. Note that the code 101 is not confusing, as it can only refer to floor 10 and room 1 and never to floor 1 and room 1, as it has the code 11. How many codes are confusing, including the one in the figure?
<image1>
Answer: 18
Problem: <image>Question: Erik has 4 bricks of the same size: <image1>. Which of the cubes shown below can he make with his 4 bricks?
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: C
Problem: <image>Question: How many fish will have their heads pointing towards the ring when we straighten the line?
<image1>
Answer: 6
Problem: <image>Question: When you put the 4 puzzle pieces together correctly, they form a rectangle with a calculation on it. What is the result of this calculation?
<image1>
Answer: 15
Problem: <image>Question: Alaya draws a picture of the sun. Which of the following answers is part of her picture?
<image1>
<image2>
Choices:
A. (A)
B. (B)
C. (C)
D. (D)
E. (E)
Answer: B
Problem: <image>Question: Five boys competed in a shooting challenge. Ricky scored the most points. Which target was Ricky's?
<image1>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: E
Problem: <image>Question: A measuring tape is wrapped around a cylinder. Which number should be at the place shown by the question mark?
<image1>
Answer: 48
Problem: <image>Question: Rosana has some balls of 3 different colours. Balls of the same colour have the same weight. What is the weight of each white ball $\bigcirc$ ?
<image1>
Answer: 5
Problem: <image>Question: Nisa has 3 different types of cards in a game: apple <image1>, cherry <image2> and grapes <image3>. She chooses 2 cards from the set and swaps their places. She wants to arrange the cards so that all the cards with the same fruit on are next to each other. For which set is this NOT possible?
<image4>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: A
Problem: <image>Question: Sofie wants to pick 5 different shapes from the boxes. She can only pick 1 shape from each box. Which shape must she pick from box 4?
<image1>
<image2>
Choices:
A. (A)
B. (B)
C. (C)
D. (D)
E. (E)
Answer: E
Problem: <image>Question: 18 cubes are coloured white or grey or black and are arranged as shown.
<image1>
The figures below show the white and the black parts. Which of the following is the grey part?
<image2>
<image3>
Choices:
A. (A)
B. (B)
C. (C)
D. (D)
E. (E)
Answer: E
Problem: <image>Question: The 5 balls shown begin to move simultaneously in the directions indicated by their arrows.
<image1>
When two balls going in opposite directions collide, the bigger ball swallows the smaller one and increases its value by the value of the smaller ball. The bigger ball continues to move in its original direction, as shown in the following example.
<image2>
What is the final result of the collisions of the 5 balls shown?
<image3>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: C
Problem: <image>Question: On a tall building there are 4 fire escape ladders, as shown. The heights of 3 ladders are at their tops. What is the height of the shortest ladder?
<image1>
Answer: 20
Problem: <image>Question: Nora plays with 3 cups on the kitchen table. She takes the left-hand cup, flips it over, and puts it to the right of the other cups. The picture shows the first
move. What do the cups look like after 10 moves?
<image1>
<image2>
Choices:
A. (A)
B. (B)
C. (C)
D. (D)
E. (E)
Answer: B
Problem: <image>Question: Eva has the 5 stickers shown: <image1>. She stuck one of them on each of the 5 squares of this board <image2> so that <image3> is not on square 5, <image4> is on square 1, and <image5> is adjacent to <image6> and <image7>. On which square did Eva stick <image5>?
Answer: 4
Problem: <image>Question: 7 cards are arranged as shown. Each card has 2 numbers on with 1 of them written upside down. The teacher wants to rearrange the cards so that the sum of the numbers in the top row is the same as the sum of the numbers in the bottom row. She can do this by turning one of the cards upside down. Which card must she turn?
<image1>
Choices:
A. A
B. B
C. D
D. F
E. G
Answer: E
Problem: <image>Question: The numbers 1 to 9 are placed in the squares shown with a number in each square. The sums of all pairs of neighbouring numbers are shown. Which number is placed in the shaded square?
<image1>
Answer: 7
Problem: <image>Question: Mia throws darts at balloons worth 3, 9, 13, 14 and 18 points. She scores 30 points in total. Which balloon does Mia definitely hit?
<image1>
Answer: 3
Problem: <image>Question: Each of the 5 boxes contains either apples or bananas, but not both. The total weight of all the bananas is 3 times the weight of all the apples. Which boxes contain apples?
<image1>
Choices:
A. 1 and 2
B. 2 and 3
C. 2 and 4
D. 3 and 4
E. 1 and 4
Answer: E
Problem: <image>Question: Elena wants to write the numbers from 1 to 9 in the squares shown. The arrows always point from a smaller number to a larger one. She has already written 5 and 7. Which number should she write instead of the question mark?
<image1>
Answer: 6
Problem: <image>Question: Martin placed 3 different types of objects, hexagons <image1>, squares <image2> and triangles <image3>, on sets of scales, as shown.
<image4>
What does he need to put on the left-hand side on the third set of scales for these scales to balance?
Choices:
A. 1 square
B. 2 squares
C. 1 hexagon
D. 1 triangle
E. 2 triangles
Answer: A
Problem: <image>Question: The bee wants to get to the flower. Each arrow indicates a move to one neighbouring square. Which path can the bee fly to get to the flower?
<image1>
Choices:
A. $\downarrow \rightarrow \rightarrow \downarrow \downarrow \downarrow$
B. $\downarrow \downarrow \rightarrow \downarrow \downarrow \rightarrow$
C. $\rightarrow \downarrow \rightarrow \downarrow \rightarrow \rightarrow$
D. $\rightarrow \rightarrow \downarrow \downarrow \downarrow \downarrow$
E. $\rightarrow \downarrow \rightarrow \downarrow \downarrow \rightarrow$
Answer: E
Problem: <image>Question: One of the five coins $A, B, C, D$ or $E$ shall be placed in an empty square so that there are exactly two coins in each row and in each column. Which coin should be moved?
<image1>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: C
Problem: <image>Question: If a laser beam hits a mirror it changes its direction (see left diagram). Each mirror has mirrored sides on both sides. At which letter does the laser beam end?
<image1>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: B
Problem: <image>Question: Kengu jumps on the number line to the right (see diagram). He first makes one big jump and then two little jumps in a row and keeps repeating the same thing over and over again. He starts at 0 and ends at 16. How many jumps does Kengu make in total?
<image1>
Answer: 12
Problem: <image>Question: In the diagram below two neighbouring squares are never allowed to have the same number. Which puzzle piece has to be placed in the gap so that this rule is followed?
<image1>
<image2>
Choices:
A. (A)
B. (B)
C. (C)
D. (D)
E. (E)
Answer: D
Problem: <image>Question: John uses some building blocks to form a work of art. What does John see when he looks at his work of art from above?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: C
Problem: <image>Question: Five cars are labelled with the numbers 1 to 5 . They drive in the direction of the arrow.
<image1>
First the last car overtakes the two cars in front of it.
Then the now second to last car overtakes the two in front of it.
In the end the car that is now in the middle overtakes the two in front of it.
In which order do the cars now drive?
Choices:
A. $1,2,3,4,5$
B. $2,1,3,5,4$
C. $2,1,5,3,4$
D. $3,1,4,2,5$
E. $4,1,2,5,3$
Answer: B
Problem: <image>Question: The members of a family of kangaroos are 2, 4, 5, 6, 8 and 10 years old. Four of them are 22 years old when added together. How old are the other two kangaroos?
<image1>
Choices:
A. 2 and 8
B. 4 and 5
C. 5 and 8
D. 6 and 8
E. 6 and 10
Answer: C
Problem: <image>Question: Mosif has filled a table with numbers (see diagram). When he adds the numbers in each row and in each column together, the result should always be the same. He has however, made a mistake. In order to get the same result every time he has to change one single number. Which number does Mosif have to change?
<image1>
Answer: 3
Problem: <image>Question: Aladdin's carpet has the shape of a square. Along each edge there are two rows of dots (see diagram). The number of points is the same along each edge. How many dots in total does the carpet have?
<image1>
Answer: 32
Problem: <image>Question: Johanna folds a piece of paper with the numbers 1 to 36 in half twice (see diagrams).
<image1>
Then she stabs a hole through all four layers at the same time (see diagram on the right). Which four numbers does she pierce in doing so?
Choices:
A. $8,11,26,29$
B. $14,16,21,23$
C. $14,17,20,23$
D. $15,16,21,22$
E. $15,17,20,22$
Answer: C
Problem: <image>Question: Jan sends five postcards to his friends during his holiday.
The card for Michael does not have ducks.
The card for Lexi shows a dog.
The card for Clara shows the sun.
The card for Heidi shows kangaroos.
The card for Paula shows exactly two animals.
Which card does Jan send to Michael?
<image1>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: A
Problem: <image>Question: Wanda chooses some of the following shapes. She says: "I have chosen exactly 2 grey, 2 big and 2 round shapes." What is the minimum number of shapes Wanda has chosen?
<image1>
Answer: 3
Problem: <image>Question: The little caterpillar <image1> rolls up to go to sleep. What could it look like then?
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: A
Problem: <image>Question: A pyramid is built from cubes (see diagram)
All cubes have side length $10 \mathrm{~cm}$.
An ant crawls along the line drawn across the pyramid (see diagram).
How long is the path taken by the ant?
<image1>
Choices:
A. $30 \mathrm{~cm}$
B. $60 \mathrm{~cm}$
C. $70 \mathrm{~cm}$
D. $80 \mathrm{~cm}$
E. $90 \mathrm{~cm}$
Answer: E
Problem: <image>Question: A road leads away from each of the six houses (see diagram). A hexagon showing the roads in the middle is however, missing. Which hexagons fit in the middle so
<image1>that one can travel from $A$ to $B$ and to $E$, but not to $D$?
Choices:
A. 1 and 2
B. 1 and 4
C. 1 and 5
D. 2 and 3
E. 4 and 5
Answer: C
Problem: <image>Question: Ahmed and Sara move from point $A$ in the direction shown with the same speed. Ahmed walks around the square garden and Sara walks around the rectangular garden. How many rounds does Ahmed have to walk to meet Sara in point $A$ again for the first time?
<image1>
Answer: 3
Problem: <image>Question: The big cube is made up of three different kinds of building blocks (see diagram). How many of the little white cubes are needed for this big cube?
<image1>
Answer: 11
Problem: <image>Question: Under cards with the same colour, the same number is always found. If the three hidden numbers in one row are added, one obtains the number to the right of the row. Which number is hidden under the black card?
<image1>
Answer: 12
Problem: <image>Question: Five children each light a candle at the same time. Lisa blows out the candles at different times. Now they look as shown in the picture.
<image1>
Which candle did Lisa blow out first?
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: D
Problem: <image>Question: The two markers with a question mark have the same value.
<image1>
Which value do you have to use instead of the question mark so that the calculation is correct?
Answer: 5
Problem: <image>Question: A black disc with two holes is placed on top of a dial of a watch.
The black disc is turned.
Which two numbers can be seen at the same time?
<image1>
Choices:
A. 4 and 9
B. 5 and 10
C. 5 and 9
D. 6 and 9
E. 7 and 12
Answer: C
Problem: <image>Question: Alice has these four jigsaw pieces:
<image1>
Which two can she put together to form this square?
Choices:
A. 1 and 2
B. 1 and 3
C. 2 and 3
D. 2 and 4
E. 1 and 4
Answer: E
Problem: <image>Question: Maria switches the lights on and off according to the given plan.
<image1>
For how many minutes in total are there exactly two lights on at the same time?
Answer: 8
Problem: <image>Question: Christoph folds a see-through piece of foil along the dashed line. What can he then see?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: A
Problem: <image>Question: Anna has four discs of different sizes. She wants to build a tower using 3 discs. A smaller disc always has to lie on top of a bigger disc. How many ways are there for Anna to build this tower?
<image1>
Answer: 4
Problem: <image>Question: Daniel sticks these two pieces of paper <image1> on this black circle: <image2> The two pieces of paper are not allowed to overlap. Which picture does he get?
<image3>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: E
Problem: <image>Question: Using the pieces $A, B, C, D$ and $E$ one can fill this shape completely: Which of the pieces lies on the dot?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: E
Problem: <image>Question: The six weights of a scale weigh $1 \mathrm{~kg}, 2 \mathrm{~kg}, 3 \mathrm{~kg}, 4 \mathrm{~kg}, 5 \mathrm{~kg}$ and $6 \mathrm{~kg}$. Rosi places five weights on the two scale pans so that they are balanced. The sixth weight is left aside. Which weight is left aside?
<image1>
Choices:
A. $1 \mathrm{~kg}$
B. $2 \mathrm{~kg}$
C. $3 \mathrm{~kg}$
D. $4 \mathrm{~kg}$
E. $5 \mathrm{~kg}$
Answer: A
Problem: <image>Question: The diagram shows four cars 1, 2, 3 and 4. The arrows show where the cars move to in 5 seconds. Which cars will crash into each other?
<image1>
Choices:
A. 1 and 2
B. 1 and 3
C. 1 and 4
D. 2 and 3
E. 3 and 4
Answer: D
Problem: <image>Question: North of Straße A (street A) there are 7 houses. East of Straße B (street B) there are 8 houses. South of Straße A (street A) there are 5 houses. How many houses are there West of Straße B (street B)?
<image1>
Answer: 4
Problem: <image>Question: 6 beavers and 2 kangaroos are standing on the fields in this order: Of three animals in a row there is always exactly one kangaroo. On which of these numbers stands a kangaroo?
<image1>
Answer: 3
Problem: <image>Question: Hanni wants to colour in the circles in the diagram. When two circles are connected by a line they should have different colours. What is the minimum number of colours she needs?
<image1>
Answer: 3
Problem: <image>Question: A building block is made up of five identical rectangles: <image1>
How many of the patterns shown below can be made with two such building blocks without overlap?
<image2>
<image3>
<image4>
<image5>
<image6>
Answer: 4
Problem: <image>Question: An underground line has the six stations A, B, C, D, E and F. The train stops at every station. After reaching the end of the line $A$ or $F$ the train continues in the opposite direction. The train conductor starts his journey in station B. His first stop is in station C. In which station will be his $46^{\text {th}}$ stop?
<image1>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: D
Problem: <image>Question: Rebecca folds a square piece of paper twice. Then she cuts off one corner as you can see in the diagram.
<image1>
Then she unfolds the paper. What could the paper look like now?
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: B
Problem: <image>Question: Five clocks are hanging on the wall. One clock is one hour ahead. Another one is one hour late and one is correct. Two clocks have stopped working. Which clock shows the correct time?
<image1>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: D
Problem: <image>Question: Adam has 9 marbles and Brenda also has 9 marbles. Together they have 8 white and 10 black marbles. Brenda has twice as many black marbles as white marbles. How many black marbles does Adam have?
<image1>
Answer: 4
Problem: <image>Question: Else has two machines R and S. If she puts a square piece of paper into machine $R$ it is rotated: <image1>
If she puts the piece of paper in machine $S$ it is printed on: <image2>
She wants to produce the following picture: <image3>
In which order does Else use the two machines so that she gets this picture?
<image4>
Choices:
A. SRR
B. RSR
C. RSS
D. RRS
E. SRS
Answer: B
Problem: <image>Question: A teacher wants to write the numbers from 1 to 7 into the circles. He writes exactly one number in each circle. When he adds up the two numbers of circles that are next to each other, he gets the number that is written between the two circles.
Which number does he write in the circle with the question mark?
<image1>
Answer: 4
Problem: <image>Question: Maria colours exactly 5 cells of this grid <image1> in grey. Then she has her 5 friends guess which cells she has coloured in and their answers are the five patterns $A, B, C, D$ and $E$. Maria looks at the patterns and says: "One of you is right. The others have each guessed exactly four cells correctly." Which pattern did Maria paint?
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: E
Problem: <image>Question: The sum of the numbers in each of the rings should be 55. Which number is $X$?
<image1>
Answer: 10
Problem: <image>Question: The square in the picture consists of two smaller squares and two rectangles of area $18 \mathrm{~cm}^{2}$ each. The area of one of smaller rectangles is $81 \mathrm{~cm}^{2}$. What is the length (in $\mathrm{cm}$ ) of side of the biggest square?
<image1>
Answer: 11
Problem: <image>Question: The picture shows the clown Dave dancing on top of two balls and one cubic box. The radius of the lower ball is $6 \mathrm{dm}$, the radius of the upper ball is three times less. The side of the cubic box is $4 \mathrm{dm}$ longer than the radius of the upper ball. At what height (in $\mathrm{dm}$ ) above the ground is the clown Dave standing?
<image1>
Answer: 22
Problem: <image>Question: The rectangle in the picture consists of 7 squares. The lengths of the sides of some of the squares are shown. Square $\mathrm{K}$ is the biggest one, square $\mathrm{L}$ -- the smallest one. How many times is the area of $\mathrm{K}$ bigger than the area of L?
<image1>
Answer: 25
Problem: <image>Question: Square $A B C D$ is comprised of one inner square (white) and four shaded congruent rectangles. Each shaded rectangle has a perimeter of $40 \mathrm{~cm}$. What is the area (in $\mathrm{cm}^{2}$ ) of square $A B C D$ ?
<image1>
Answer: 400
Problem: <image>Question: The composite board shown in the picture consists of 20 fields $1 \times 1$. How many possibilities are there exist to cover all 18 white fields with 9 rectangular stones $1 \times 2$ ? (The board cannot be turned. Two possibilities are called different if at least one stone lies in another way.)
<image1>
Answer: 4
Problem: <image>Question: The square was cut out from a page in a squared exercise book. Then two figures in the picture were cut out from the square. Which ones?
<image1>
Choices:
A. 1 and 3
B. 2 and 4
C. 2 and 3
D. 1 and 4
E. Impossible to cut out
Answer: C
Problem: <image>Question: Walter displayed all the integers from 0 to 109 according to some simple rule. Here is the beginning of his 5-column numeral chart. Which of the following elements could not be the a part of Walter's chart?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: B
Problem: <image>Question: What is the length (in $\mathrm{cm}$ ) of the line (see picture) connecting vertices $M$ and $N$ of the square?
<image1>
Answer: 10100
Problem: <image>Question: Every figure in the picture replaces some digit. What is the sum $\square+\bigcirc$ ?
<image1>
Answer: 7
Problem: <image>Question: The figure in the drawing consists of five isosceles right triangles of the same size. Find the area (in $\mathrm{cm}^{2}$ ) of the shaded figure.
<image1>
Answer: 45
Problem: <image>Question: Caroline wants to write the numbers 1, 2, 3, 4 in the square $4 \times 4$ in such a way that every row and every column has each number. You see how she started. What number must be put in the place of $x$?
<image1>
Answer: 3
Problem: <image>Question: You have two identical pieces that you can turn around but not upside down. Which picture can you not make with these two pieces?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: D
Problem: <image>Question: Harry folds a sheet of paper five times. Then he makes a hole in the folded paper, after which he unfolds it.
<image1>
How many holes has the unfolded paper?
Answer: 32
Problem: <image>Question: Different figures represent different digits. Find the digit corresponding to the square.
<image1>
Answer: 6
Problem: <image>Question: What is the smallest number of little squares that need to be painted to get at least one axis of symmetry in the picture?
<image1>
Answer: 2
Problem: <image>Question: We have cut off one corner of a cube. Which of the developments below is the development of the remaining part?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: E
Problem: <image>Question: Snail quadruplets have gone hiking on a path paved with identical rectangular tiles. The shape and length of each snail's trip is shown below.
<image1>
How many decimeters has the snail Tin hiked?
Answer: 35
Problem: <image>Question: In the diagram drawn on the square grid, find the ratio of the unshaded area to the shaded area.
<image1>
Choices:
A. $\frac{1}{4}$
B. $\frac{1}{5}$
C. $\frac{1}{6}$
D. $\frac{2}{5}$
E. $\frac{2}{7}$
Answer: A
Problem: <image>Question: You write a number in each square as shown in the square figure. Then, the number $x$ cannot be:
<image1>
Answer: 128
Problem: <image>Question: A butterfly sat down on my correctly solved exercise: 2005-205=25+<image1>
What number is the butterfly covering?
Answer: 1775
Problem: <image>Question: The diagram shows a cube with sides of length $12 \mathrm{~cm}$. An ant moves on the cube surface from point $M$ to point $N$ following the route shown. Find the length of ant's path.
<image1>
Choices:
A. 40 cm
B. 48 cm
C. 50 cm
D. 60 cm
E. It is impossible to determine
Answer: D
Problem: <image>Question: Five cards are lying on the table in the order 1, 3, 5, 4, 2. You must get the cards in the order 1, 2, 3, 4, 5. Per move, any two cards may be interchanged. How many moves do you need at least?
<image1>
Answer: 2
Problem: <image>Question: In the diagram you see the rectangular garden of Green's family. It has an area of $30 \mathrm{~m}^{2}$ and is divided into three rectangular parts. One side of the part where flowers are growing has a length of $2 \mathrm{~m}$. Its area is $10 \mathrm{~m}^{2}$. The part with strawberries has one side of length $3 \mathrm{~m}$. What is the area of the part where vegetables are growing?
<image1>
Choices:
A. $4 \mathrm{~m}^{2}$
B. $6 \mathrm{~m}^{2}$
C. $8 \mathrm{~m}^{2}$
D. $10 \mathrm{~m}^{2}$
E. $12 \mathrm{~m}^{2}$
Answer: C
Problem: <image>Question: There are seven squares in the picture. How many more triangles than squares are there in the picture?
<image1>
Answer: 3
Problem: <image>Question: You fill the diagram with integers so that every number (except those from the lower row) is equal to the sum of two neighbouring numbers below it. Which number should replace $x$?
<image1>
Answer: 82
Problem: <image>Question: In the picture the small equilateral triangles have an area of 1 unit. What is the area of the shaded region?
<image1>
Answer: 22.5