Yuting6/geoqa-r1v-8k-rotated huggingface dataset:
Problem: <image>Question: A terrace is covered with square tiles of different sizes. The smallest tile has a perimeter of $80 \mathrm{~cm}$. A snake lay down along the edges of the tiles (see diagram). How long is the snake? <image1>
Choices:
A. $380 \mathrm{~cm}$
B. $400 \mathrm{~cm}$
C. $420 \mathrm{~cm}$
D. $440 \mathrm{~cm}$
E. $1680 \mathrm{~cm}$
Answer: C
Problem: <image>Question: The picture of a digital watch can be seen in a mirror:
<image1> Which picture of the watch can be seen in the mirror 30 minutes later?
Choices:
A. $12:22$
B. $12:55$
C. $15:15$
D. $15:55$
E. $21:21$
Answer: D
Problem: <image>Question: The sums of the numbers in the white and in the grey fields should be equally big. Which two numbers have to be swapped so that the sums are equally big? <image1>
Choices:
A. 1 and 11
B. 2 and 8
C. 3 and 7
D. 4 and 13
E. 7 and 13
Answer: A
Problem: <image>Question: The big rectangle is made up of five small rectangles (see diagram). Lukas wants to colour in the small rectangles in red, blue and yellow. Two rectangles next to each other should be coloured in different colours.
<image1> How many ways are there for Lukas to do that?
Answer: 6
Problem: <image>Question: 4 posts are placed along a $120 \mathrm{~m}$ long running track. How many more posts have to be placed so that the running track is split into equally long sections that way? <image1>
Answer: 17
Problem: <image>Question: In a game one is allowed to take (some or all) building blocks from the top of a stack of building blocks, turn them upside down and place them back in the same position within one move. Goran starts with this stack of building blocks: <image1> In the end all building blocks should be ordered according to size. What is the minimum number of moves Goran needs to make?
Answer: 3
Problem: <image>Question: A rabbit, a beaver and a kangaroo are having a competition. All three begin at the same time from the "Start" and hop in the same direction. The beaver always moves one position forwards with each jump. The rabbit always moves two positions forwards with one jump and the kangaroo always three positions. Whoever takes the least amount of jumps to land exactly in the position labelled "Ziel“ is the winner. <image1> Who wins the competition?
Choices:
A. Kangaroo and rabbit
B. Rabbit
C. Kangaroo
D. Beaver
E. Kangaroo and beaver
Answer: E
Problem: <image>Question: Tina draws shapes into each field of the pyramid. Each field in the second and third row contains exactly the shapes of the two fields below. Some fields are already done. Which shapes does she draw into the empty field of the bottom row? <image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: D
Problem: <image>Question: A tower is made up of bricks that are labelled with the numbers from 1 to 50 from bottom to top. Bob uses these bricks to build a new tower. Each time he takes the two topmost bricks off the old tower and places them down on top of the new tower without changing their order (see diagram). Which two bricks lie on top of each other when he is finished with the re-arrangement? <image1>
Choices:
A. 29 and 28
B. 34 and 35
C. 29 and 26
D. 31 and 33
E. 27 and 30
Answer: E
Problem: <image>Question: Martin has three cards that are labelled on both sides with a number. Martin places the three cards on the table without paying attention to back or front. He adds the three numbers that he can then see. How many different sums can Martin get that way?
<image1>
Choices:
A. 3
B. 5
C. 6
D. 9
E. A different amount.
Answer: E
Problem: <image>Question: Anna has two machines $R$ and $S$. If she places a square piece of paper in machine $R$ it is rotated $90^{\circ}$ in a clockwise direction. <image1> (Hint: Note the marking in the corner!) If she places the piece of paper in machine $S$, it gets printed on. <image2> In which order does Anna use the two machines so that this picture is made? <image3>
Choices:
A. SRRR
B. RSRR
C. SRSR
D. RRRS
E. SRRS
Answer: B
Problem: <image>Question: Monika wants to find a path through the labyrinth from 'Start' to 'Ziel'. She has to stick to the following rules: She is only allowed to move horizontally and vertically respectively. She has to enter every white circle exactly once but is not allowed to enter a black circle. In which direction does Monika have to move forwards when she reaches the circle marked with $x$ ? <image1>
Choices:
A. $\downarrow$
B. $\uparrow$
C. $\rightarrow$
D. $\leftarrow$
E. there are several possibilities
Answer: A
Problem: <image>Question: A folded napkin was cut through (see picture). What does it look like when unfolded?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: C
Problem: <image>Question: The composite board shown in the picture consists of 44 fields $1 \times 1$. How many possibilities are there to cover all 40 white fields with 20 rectangular stones $1 \times 2$? (The board cannot be turned. Two possibilities are different if at least one stone lies in another way.)
<image1>
Answer: 16
Problem: <image>Question: Lying on a table, there is a transparent square sheet of film with the letter $\mathbf{y}$ written on it. We turn the sheet $90^{\circ}$ clockwise, then turn it over from its right side, then turn it $180^{\circ}$ counterclockwise. What do we now see?
<image1>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: A
Problem: <image>Question: Jeffrey shoots three arrows at each of four identical targets. He scores 29 points on the first target, 43 on the second and 47 on the third. How many points does Jeffrey score on the last target?
<image1>
Answer: 36
Problem: <image>Question: Two quadrates with the same size cover a circle, the radius of which is $3 \mathrm{~cm}$. Find the total area (in $\mathrm{cm}^{2}$ ) of the shaded figure.
<image1>
Choices:
A. $8(\pi-1)$
B. $6(2 \pi-1)$
C. $9 \pi-25$
D. $9(\pi-2)$
E. $\frac{6 \pi}{5}$
Answer: D
Problem: <image>Question: A rectangular parallelepiped was composed of 3 pieces, each consisting of 4 little cubes. Then one piece was removed (see picture). Which one?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: D
Problem: <image>Question: In a rectangle $A B C D$, let $P, Q, R$ and $S$ be the midpoints of sides $A B, B C, C D$ and $A D$, respectively, and let $T$ be the midpoint of segment $R S$. Which fraction of the area of $A B C D$ does triangle $P Q T$ cover?
<image1>
Choices:
A. $\frac{5}{16}$
B. $\frac{1}{4}$
C. $\frac{1}{5}$
D. $\frac{1}{6}$
E. $\frac{3}{8}$
Answer: B
Problem: <image>Question: Carl composed the figure shown on the left side of the drawing from the smaller three-square and four-square figures shown on the right side. The smaller figures can be turned around, but not turned over. What is the smallest number of three-square figures needed for that?
<image1>
Answer: 2
Problem: <image>Question: A square is divided into 25 small squares (see the picture). Find the measure of the angle which is the sum of the angles $M A N, M B N, M C N, M D N, M E N$.
<image1>
Choices:
A. 30°
B. 45°
C. 60°
D. 75°
E. 90°
Answer: B
Problem: <image>Question: We are going to make a spiral of isosceles triangles. We'll start with the shaded triangle $B A C$, which has a top angle $\angle B A C=100^{\circ}$, and move counterclockwise. Let $\triangle A B C$ have number 0. Every of the next triangles (with numbers 1, 2, $3, \ldots$ ) will have exactly one edge adjoining the previous one (see the picture). What will be the number of the first triangle which precisely covers triangle $\mathrm{nr}$. 0?
<image1>
Answer: 18
Problem: <image>Question: In triangle $A B C$ (see picture) $A B=A C, A E=A D$, and $\angle B A D=30^{\circ}$. What is the measure of angle $C D E$?
<image1>
Choices:
A. $10^{\circ}$
B. $15^{\circ}$
C. $20^{\circ}$
D. $25^{\circ}$
E. $30^{\circ}$
Answer: B
Problem: <image>Question: An equilateral triangle $A C D$ is rotated counterclockwise around point $A$. At what angle has it been rotated unen it covers equilateral triangle $A B C$ for the first time?
<image1>
Choices:
A. $60^{\circ}$
B. $120^{\circ}$
C. $180^{\circ}$
D. $240^{\circ}$
E. $300^{\circ}$
Answer: E
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 of the numbers. You see how she started. How many of the 4 numbers can be written in place of $x$?
<image1>
Answer: 2
Problem: <image>Question: The section of a cube by a plane generates a plane figure. I have plotted this section in the development of the cube (see the picture). Can you find out what figure it is?
<image1>
Choices:
A. An equilateral triangle
B. A rectangle, but not a square
C. A right triangle
D. A square
E. A hexagon
Answer: A
Problem: <image>Question: The point $O$ is the center of the circle in the picture. What is the diameter of the circle?
<image1>
Answer: 10
Problem: <image>Question: We link rings together as shown in the figure below; the length of the chain is $1.7 \mathrm{~m}$. How many rings are there?
<image1>
Answer: 42
Problem: <image>Question: In the picture a square $A B C D$ and two semicircles with diameters $A B$ and $A D$ have been drawn. If $A B=2$, what is the area of the shaded region?
<image1>
Answer: 8
Problem: <image>Question: In the picture we have 11 fields.
<image1>
In the first field there is a 7, and in the ninth field we have a 6. What positive integer has to be written in the second field for the following condition to be valid: the sum of any three adjoining fields is equal to 21?
Answer: 8
Problem: <image>Question: In a square with sides of length 6 the points $A$ and $B$ are on a line joining the midpoints of the opposite sides of the square (see the figure). When you draw lines from $A$ and $B$ to two opposite vertices, you divide the square in three parts of equal area. What is the length of $A B$?
<image1>
Answer: 4
Problem: <image>Question: The diagram shows the ground plan of a room. The adjacent walls are perpendicular to each other. What is the area of the room?
<image1>
Choices:
A. $2 a b+a(b-a)$
B. $3 a(a+b)-a^{2}$
C. $3 a^{2} b$
D. $3 a(b-a)+a^{2}$
E. $3 a b$
Answer: E
Problem: <image>Question: In the diagram, the five circles have the same radii and touch as shown. The square joins the centres of the four outer circles. The ratio of the area of the shaded part of all five circles to the area of the unshaded parts of the circles is:
<image1>
Choices:
A. $1: 3$
B. $1: 4$
C. $2: 5$
D. $2: 3$
E. $5: 4$
Answer: D
Problem: <image>Question: Two rectangles $A B C D$ and $D B E F$ are shown in the figure. What is the area (in $\mathrm{cm}^{2}$ ) of the rectangle $D B E F$?
<image1>
Answer: 12
Problem: <image>Question: Let $a$ and $b$ be two shorter sides of the right-angled triangle. Then the sum of the diameter of the incircle and that of the circumcircle of this triangle is equal to:
<image1>
Choices:
A. $\sqrt{a^{2}+b^{2}}$
B. $\sqrt{a b}$
C. $0.5(a+b)$
D. $2(a+b)$
E. $a+b$
Answer: E
Problem: <image>Question: A particle moves through the first quadrant of the shown figure as follows. During the first minute it moves from the origin to $(1 ; 0)$. Thereafter it continues to follow the directions indicated in the figure, going back and forth between the positive part of the $x$ and $y$ axes, moving one unit of distance parallel to an axis in each minute. Which point will the particle reach after exactly 2 hours?
<image1>
Choices:
A. $(10 ; 0)$
B. $(1 ; 11)$
C. $(10 ; 11)$
D. $(2 ; 10)$
E. $(11 ; 11)$
Answer: A
Problem: <image>Question: The point $O$ is the centre of a regular pentagon. How much of the pentagon is shaded?
<image1>
Choices:
A. $10 \%$
B. $20 \%$
C. $25 \%$
D. $30 \%$
E. $40 \%$
Answer: D
Problem: <image>Question: Which of the following nets has a cube in the right picture?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: E
Problem: <image>Question: The solid in the picture is created from two cubes. The small cube with edges $1 \mathrm{~cm}$ long is placed on the top of a bigger cube with edges $3 \mathrm{~cm}$ long. What is the surface area of this solid?
<image1>
Choices:
A. $56 \mathrm{~cm}^{2}$
B. $58 \mathrm{~cm}^{2}$
C. $59 \mathrm{~cm}^{2}$
D. $60 \mathrm{~cm}^{2}$
E. $64 \mathrm{~cm}^{2}$
Answer: B
Problem: <image>Question: A rectangle on the right is divided into 7 squares. The sides of the grey squares are all 8. What is the side of the great white square?
<image1>
Answer: 18
Problem: <image>Question: Max and Moritz have drawn a square $5 \times 5$ and marked the centres of the small squares. Afterwards, they draw obstacles and then find out in how many ways it is possible to go from $A$ to $B$ using the shortest way avoiding the obstacles and going from centre to centre only vertically and horizontally. How many shortest paths are there from $A$ to $B$ under these conditions?
<image1>
Answer: 12
Problem: <image>Question: Belinda is making patterns with toothpicks according to the schema of the figure. How many toothpicks does Belinda add to the 30th pattern to make the 31 st?
<image1>
Answer: 124
Problem: <image>Question: What is the smallest number of dots that need be removed from the pattern shown, so that no three of the remaining dots are at the vertices of an equilateral triangle?
<image1>
Answer: 4
Problem: <image>Question: The first row shows 11 cards, each with two letters. The second row shows rearangement of the cards. Which of the following could appear on the bottom line of the second row?
<image1>
Choices:
A. ANJAMKILIOR
B. RLIIMKOJNAA
C. JANAMKILIRO
D. RAONJMILIKA
E. ANMAIKOLIRJ
Answer: E
Problem: <image>Question: What is the sum of the points on the invisible faces of the dice?
<image1>
Answer: 27
Problem: <image>Question: A small square is inscribed in a big one as shown in the figure. Find the area of the small square.
<image1>
Answer: 34
Problem: <image>Question: How many little squares at least do we have to shade in the picture on the right in order that it have an axis of symmetry?
<image1>
Answer: 3
Problem: <image>Question: There are six identical circles in the picture. The circles touch the sides of a large rectangle and one another as well. The vertices of the small rectangle lie in the centres of the four circles, as illustrated. The perimeter of the small rectangle is $60 \mathrm{~cm}$. What is the perimeter of the large rectangle?
<image1>
Choices:
A. $160 \mathrm{~cm}$
B. $140 \mathrm{~cm}$
C. $120 \mathrm{~cm}$
D. $100 \mathrm{~cm}$
E. $80 \mathrm{~cm}$
Answer: D
Problem: <image>Question: $A B C$ and $C D E$ are equal equilateral triangles. If $\angle A C D=80^{\circ}$, what is $\angle A B D$?
<image1>
Choices:
A. $25^{\circ}$
B. $30^{\circ}$
C. $35^{\circ}$
D. $40^{\circ}$
E. $45^{\circ}$
Answer: D
Problem: <image>Question: By drawing 9 segments (5 horizontal and 4 vertical) one can make a table of 12 cells. How many cells can you get maximally if you draw 15 segments?
<image1>
Answer: 42
Problem: <image>Question: Which of the following objects can be obtained by rotating in space the grey object?
<image1>
<image2>
Choices:
A. W and Y
B. X and Z
C. Only Y
D. None of these
E. W, X ir Y
Answer: A
Problem: <image>Question: Segments $O A, O B, O C$ and $O D$ are drawn from the centre $O$ of the square $K L M N$ to its sides so that $O A \perp O B$ and $O C \perp O D$ (as shown in the figure). If the side of the square equals 2, the area of the shaded region equals
<image1>
Answer: 2
Problem: <image>Question: In the picture there is a square tile with two fourths of a circle. The radius of every fourth is half the side of the tile and its length equals $5 \mathrm{dm}$. We form a large square from 16 such tiles and try to get the longest unbroken curve consisting of the fourths. How long can this continuous curve be at most?
<image1>
Choices:
A. $75 \mathrm{dm}$
B. $100 \mathrm{dm}$
C. $105 \mathrm{dm}$
D. $110 \mathrm{dm}$
E. $80 \mathrm{dm}$
Answer: D
Problem: <image>Question: How many pieces of string are there in the picture?
<image1>
Answer: 4
Problem: <image>Question: A cube has all its corners cut off, as shown. How many edges does the resulting shape have?
<image1>
Answer: 36
Problem: <image>Question: Three lines intersect at one point. Two angles are given in the figure. How many degrees does the grey angle have?
<image1>
Choices:
A. $52^{\circ}$
B. $53^{\circ}$
C. $54^{\circ}$
D. $55^{\circ}$
E. $56^{\circ}$
Answer: A
Problem: <image>Question: How many squares can be drawn by joining the dots with line segments?
<image1>
Answer: 4
Problem: <image>Question: Four tangent congruent circles of radius $6 \mathrm{~cm}$ are inscribed in a rectangle.
<image1>
If $P$ is a vertex and $Q$ and $R$ are the points of tangency, what is the area of triangle $P Q R$?
Choices:
A. $27 \mathrm{~cm}^{2}$
B. $45 \mathrm{~cm}^{2}$
C. $54 \mathrm{~cm}^{2}$
D. $108 \mathrm{~cm}^{2}$
E. $180 \mathrm{~cm}^{2}$
Answer: D
Problem: <image>Question: In an isosceles triangle $A B C(A B=A C)$, the bisector $C D$ of the angle $C$ is equal to the base $B C$. Then the angle $C D A$ is equal to
<image1>
Choices:
A. $90^{\circ}$
B. $100^{\circ}$
C. $108^{\circ}$
D. $120^{\circ}$
E. Impossible to determine
Answer: C
Problem: <image>Question: In the picture any letter stands for some digit (different letters for different digits, equal letters for equal digits). Find the largest possible value of the number KAN.
<image1>
Answer: 864
Problem: <image>Question: Four identical dice are arranged in a row (see the fig.).
<image1>
Each dice has faces with 1, 2, 3, 4, 5 and 6 points, but the dice are not standard, i.e., the sum of the points on the opposite faces of the dice is not necessarily equal to 7. What is the total sum of the points in all the 6 touching faces of the dice?
Answer: 20
Problem: <image>Question: The star shown in the picture is made by fitting together 12 congruent equilateral triangles. The perimeter of the star is $36 \mathrm{~cm}$. What is the perimeter of the grey hexagon?
<image1>
Choices:
A. $6 \mathrm{~cm}$
B. $12 \mathrm{~cm}$
C. $18 \mathrm{~cm}$
D. $24 \mathrm{~cm}$
E. $30 \mathrm{~cm}$
Answer: C
Problem: <image>Question: In the picture the large square has an area of 1. What is the area of the small black square?
<image1>
Choices:
A. $\frac{1}{100}$
B. $\frac{1}{300}$
C. $\frac{1}{600}$
D. $\frac{1}{900}$
E. $\frac{1}{1000}$
Answer: D
Problem: <image>Question: In the diagram QSR is a straight line. $\angle \mathrm{QPS}=12^{\circ}$ and $\mathrm{PQ}=\mathrm{PS}=\mathrm{RS}$. How big is $\angle \mathrm{QPR}$?
<image1>
Choices:
A. $36^{\circ}$
B. $42^{\circ}$
C. $54^{\circ}$
D. $60^{\circ}$
E. $84^{\circ}$
Answer: C
Problem: <image>Question: Which of the following is made using more than one piece of string?
<image1>
Choices:
A. I, III, IV and V
B. I, III and V
C. III, IV and V
D. all
E. None of these answers
Answer: B
Problem: <image>Question: What is the minimum number of dots that must be taken away from the picture so that no three of the remaining dots lie on a straight line?
<image1>
Answer: 3
Problem: <image>Question: What fraction of the largest square is grey?
<image1>
Choices:
A. $\frac{1}{4}$
B. $\frac{1}{5}$
C. $\frac{2}{5}$
D. $\frac{3}{8}$
E. $\frac{1}{3}$
Answer: A
Problem: <image>Question: In the diagram opposite there is an object with 6 triangular faces. On each corner there is a number (two are shown). The sum of the numbers on the corners of each face is the same. What is the sum of all 5 numbers?
<image1>
Answer: 17
Problem: <image>Question: We want to paint each square in the grid with the colours P, Q, R and S, so that neighbouring squares always have different colours. (Squares which share the same corner point also count as neighbouring.) Some of the squares are already painted. In which colour(s) could the grey square be painted?
<image1>
Choices:
A. only Q
B. only R
C. only S
D. either R or S
E. it is not possible.
Answer: D
Problem: <image>Question: The diagram opposite shows a regular nonagon. What is the size of the angle marked $\mathrm{X}$?
<image1>
Choices:
A. $40^{\circ}$
B. $45^{\circ}$
C. $50^{\circ}$
D. $55^{\circ}$
E. $60^{\circ}$
Answer: E
Problem: <image>Question: A pattern is made out of white, square tiles. The first three patterns are shown. How many tiles will be needed for the tenth pattern?
<image1>
Answer: 92
Problem: <image>Question: A beetle walks along the edges of a cube. Starting from point $P$ it first moves in the direction shown. At the end of each edge it changes the direction in which it turns, turning first right then left, then right etc. Along how many edges will it walk before it returns to point $P$?
<image1>
Answer: 6
Problem: <image>Question: The fractions $\frac{1}{3}$ und $\frac{1}{5}$ are shown on the number line. In which position should $\frac{1}{4}$ be shown?
<image1>
Choices:
A. a
B. b
C. c
D. d
E. e
Answer: A
Problem: <image>Question: A cube is cut in three directions as shown, to produce eight cuboids (each cut is parallel to one of the faces of the cube). What is the ratio of the total surface area of the eight cuboids to the surface area of the original cube?
<image1>
Choices:
A. 1:1
B. 4:3
C. 3:2
D. 2:1
E. 4:1
Answer: D
Problem: <image>Question: How many lines of symmetry does this figure have?
<image1>
Answer: 2
Problem: <image>Question: The perimeter of the figure pictured on the right is......
<image1>
Choices:
A. $3 a+4 b$
B. $3 a+8 b$
C. $6 a+4 b$
D. $6 a+6 b$
E. $6 a+8 b$
Answer: E
Problem: <image>Question: Martina draws the six cornerpoints of a regular hexagon and then connects some of them to obtain a geometric figure. Which of the following figures cannot be generated?
<image1>
Choices:
A. trapezium
B. right angled triangle
C. square
D. kite
E. obtuse triangle
Answer: C
Problem: <image>Question: In the box are seven blocks. It is possible to slide the blocks around so that another block can be added to the box. What is the minimum number of blocks that must be moved?
<image1>
Answer: 3
Problem: <image>Question: In the quadrilateral $\mathrm{ABCD}, \mathrm{AD}=\mathrm{BC}, \angle \mathrm{DAC}=50^{\circ}$, $\angle \mathrm{DCA}=65^{\circ}$ and $\angle \mathrm{ACB}=70^{\circ}$. How big is $\angle \mathrm{ABC}$?
<image1>
Choices:
A. $50^{\circ}$
B. $55^{\circ}$
C. $60^{\circ}$
D. $65^{\circ}$
E. It is not clear.
Answer: B
Problem: <image>Question: Andrea wraps a band around a piece of wood. She then turns the wood around as pictured. What does the wood now look like?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: B
Problem: <image>Question: A square is split into 4 smaller squares. All small squares should either be coloured in white or black. How many ways are there to colour the big square? (patterns are the same if they can be - as shown in the picture transformed into one another by rotation.)
<image1>
Answer: 6
Problem: <image>Question: In the figure $A B C D$ is a rectangle and $P Q R S$ a square. The area of the grey part is half as big as the area of ABCD. How long is the side PX?
<image1>
Answer: 1
Problem: <image>Question: In the figure we see semicircles with radii $2 \mathrm{~cm}, 4 \mathrm{~cm}$ or $8 \mathrm{~cm}$. What fraction of the area is grey?
<image1>
Choices:
A. $\frac{1}{3}$
B. $\frac{1}{4}$
C. $\frac{1}{5}$
D. $\frac{3}{4}$
E. $\frac{2}{3}$
Answer: B
Problem: <image>Question: In the figure there are nine regions inside the circles. The numbers 1 to 9 should be written in the regions so that the sum of the numbers in each circle is exactly 11. Which number has to go in the region with the question mark?
<image1>
Answer: 6
Problem: <image>Question: A paperstrip is folded three times in the middle. It is then opened again and looked at from the side so that one can see all 7 folds from the side at the same time. Which of the following views is not a possible result?
<image1>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: D
Problem: <image>Question: Elsa has 3 tetrahedra and 5 dice. How many faces do these eight objects have altogether?
<image1>
Answer: 42
Problem: <image>Question: In the picture on the right we can see three squares. The corners of the middle square are on the midpoints of the sides of the larger square, and the corners of the smaller square are on the midpoints of the sides of the middle square. The area of the small square is $6 \mathrm{~cm}^{2}$. What is the area of the big square?
<image1>
Choices:
A. $24 \mathrm{~cm}^{2}$
B. $18 \mathrm{~cm}^{2}$
C. $15 \mathrm{~cm}^{2}$
D. $12 \mathrm{~cm}^{2}$
E. $9 \mathrm{~cm}^{2}$
Answer: A