Yuting6/geoqa-r1v-8k-rotated huggingface dataset:
Problem: <image>Question: One of the following nets cannot be folded along the dashed lines shown to form a cube. Which one?
<image1>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: C
Problem: <image>Question: Four cars enter a roundabout at the same time, each one from a different direction, as shown in the diagram. Each car drives in a clockwise direction and leaves the roundabout before making a complete circuit. No two cars leave the roundabout by the same exit. How many different ways are there for the cars to leave the roundabout? <image1>
Answer: 9
Problem: <image>Question: Each of the four vertices and six edges of the tetrahedron $P Q R S$ is marked with one of the numbers $1,2,3,4,5,6,7,8,9$ and 11 ; so the number 10 is not used. Each number is used exactly once. Each edge is marked with the sum of the numbers at the two vertices connected by that edge. Edge $P Q$ is marked with number 9 . Which number is used to mark edge RS? <image1>
Answer: 5
Problem: <image>Question: The area of rectangle $P Q R S$ is $10 \mathrm{~cm}^{2}$. Points $M$ and $N$ are the midpoints of the sides $P Q$ and $S R$.
What is the area in $\mathrm{cm}^{2}$ of quadrilateral MRNP? <image1>
Answer: 5
Problem: <image>Question: Rachel has several square pieces of paper of area $4 \mathrm{~cm}^{2}$. She cuts each of them into smaller squares and right-angled triangles in the manner shown in the first diagram. She takes some of the pieces and makes the shape shown in the second diagram.
What is the area in $\mathrm{cm}^{2}$ of the shape? <image1>
Answer: 6
Problem: <image>Question: Carl built the shape shown using seven unit cubes. How many such cubes does he have to add to make a cube with edges of length 3 ? <image1>
Answer: 20
Problem: <image>Question: In the diagram, the area of each circle is $1 \mathrm{~cm}^{2}$. The area common to any two overlapping circles is $\frac{1}{8} \mathrm{~cm}^{2}$. What is the area of the region covered by the five circles? <image1>
Choices:
A. $4 \mathrm{~cm}^{2}$
B. $\frac{9}{2} \mathrm{~cm}^{2}$
C. $\frac{35}{8} \mathrm{~cm}^{2}$
D. $\frac{39}{8} \mathrm{~cm}^{2}$
E. $\frac{19}{4} \mathrm{~cm}^{2}$
Answer: B
Problem: <image>Question: The heart and the arrow are in the positions shown in the figure. At the same time the heart and the arrow start moving. The arrow moves three places clockwise and then stops and the heart moves four places anticlockwise and then stops. They repeat the same routine over and over again. After how many routines will the heart and the arrow land in the same place as each other for the first time? <image1>
Choices:
A. 7
B. 8
C. 9
D. 10
E. It will never happen
Answer: E
Problem: <image>Question: Five equal rectangles are placed inside a square with side $24 \mathrm{~cm}$, as shown in the diagram. What is the area in $\mathrm{cm}^{2}$ of one rectangle? <image1>
Answer: 32
Problem: <image>Question: The diagram shows the triangle $P Q R$ in which $R H$ is a perpendicular height and $P S$ is the angle bisector at $P$. The obtuse angle between $R H$ and $P S$ is four times angle $S P Q$. What is angle $R P Q$ ? <image1>
Choices:
A. $30^{\circ}$
B. $45^{\circ}$
C. $60^{\circ}$
D. $75^{\circ}$
E. $90^{\circ}$
Answer: C
Problem: <image>Question: Janet enters all the digits from 1 to 9 in the cells of a $3 \times 3$ table, so that each cell contains one digit. She has already entered 1,2,3 and 4, as shown. Two numbers are considered to be 'neighbours' if their cells share an edge. After entering all the numbers, she notices that the sum of the neighbours of 9 is 15 . What is the sum of the neighbours of 8 ? <image1>
Answer: 27
Problem: <image>Question: A $5 \times 5$ square is made from $1 \times 1$ tiles, all with the same pattern, as shown. Any two adjacent tiles have the same colour along the shared edge. The perimeter of the $5 \times 5$ square consists of black and white segments of length 1 . What is the smallest possible number of black segments on the perimeter of the
<image1>
$5 \times 5$ square?
Answer: 5
Problem: <image>Question: Quadrilateral $P Q R S$ has right angles at vertices $P$ and $Q$ only. The numbers show the areas in $\mathrm{cm}^{2}$ of two of the triangles. What is the area in $\mathrm{cm}^{2}$ of $P Q R S$ ? <image1>
Answer: 45
Problem: <image>Question: My umbrella has KANGAROO written on top as shown in the diagram. Which one of the following pictures also shows my umbrella?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: E
Problem: <image>Question: Four identical small rectangles are put together to form a large rectangle as shown. The length of a shorter side of each small rectangle is $10 \mathrm{~cm}$. What is the length of a longer side of the large rectangle? <image1>
Choices:
A. $50 \mathrm{~cm}$
B. $40 \mathrm{~cm}$
C. $30 \mathrm{~cm}$
D. $20 \mathrm{~cm}$
E. $10 \mathrm{~cm}$
Answer: B
Problem: <image>Question: In the diagram, the centre of the top square is directly above the common edge of the lower two squares. Each square has sides of length $1 \mathrm{~cm}$. What is the area of the shaded region? <image1>
Choices:
A. $\frac{3}{4} \mathrm{~cm}^{2}$
B. $\frac{7}{8} \mathrm{~cm}^{2}$
C. $1 \mathrm{~cm}^{2}$
D. $1 \frac{1}{4} \mathrm{~cm}^{2}$
E. $1 \frac{1}{2} \mathrm{~cm}^{2}$
Answer: C
Problem: <image>Question: A bush has 10 branches. Each branch has either 5 leaves only or 2 leaves and 1 flower. Which of the following could be the total number of leaves the bush has? <image1>
Choices:
A. 45
B. 39
C. 37
D. 31
E. None of A to D
Answer: E
Problem: <image>Question: One corner of a square is folded to its centre to form an irregular pentagon as shown in the diagram. The area of the square is 1 unit greater than the area of the pentagon. What is the area of the square? <image1>
Answer: 8
Problem: <image>Question: Luis wants to make a pattern by colouring the sides of the triangles shown in the diagram. He wants each triangle to have one red side, one green side and one blue side. Luis has already coloured some of the sides as shown. What colour can he use for the side marked $x$ ? <image1>
Choices:
A. only green
B. only blue
C. only red
D. either blue or red
E. The task is impossible
Answer: A
Problem: <image>Question: Ria wants to write a number in each of the seven bounded regions in the diagram. Two regions are neighbours if they share part of their boundary. The number in each region is to be the sum of the numbers in all of its neighbours. Ria has already written in two of the numbers, as shown.
What number must she write in the central region?
<image1>
Answer: 6
Problem: <image>Question: A square with area $30 \mathrm{~cm}^{2}$ is divided in two by a diagonal and then into triangles as shown. The areas of some of these triangles are given in the diagram (which is not drawn to scale). Which part of the diagonal is the longest? <image1>
Choices:
A. $a$
B. $b$
C. $C$
D. $d$
E. $e$
Answer: D
Problem: <image>Question: Andrew has seven pieces of wire of lengths $1 \mathrm{~cm}, 2 \mathrm{~cm}, 3 \mathrm{~cm}, 4 \mathrm{~cm}$, $5 \mathrm{~cm}, 6 \mathrm{~cm}$ and $7 \mathrm{~cm}$. He bends some of the pieces to form a wire frame in the shape of a cube with edges of length $1 \mathrm{~cm}$ without any overlaps. What is the smallest number of these pieces that he can use? <image1>
Answer: 4
Problem: <image>Question: The triangle in the diagram contains a right angle. What is the sum of the other two marked angles on the diagram? <image1>
Choices:
A. $150^{\circ}$
B. $180^{\circ}$
C. $270^{\circ}$
D. $320^{\circ}$
E. $360^{\circ}$
Answer: C
Problem: <image>Question: Joanna turns over the card shown about its lower edge and then about its right-hand edge, as indicated in the diagram.
<image1>
What does she see?
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: B
Problem: <image>Question: What is the total area in $\mathrm{cm}^{2}$ of the shaded region? <image1>
Answer: 100
Problem: <image>Question: Four towns $P, Q, R$ and $S$ are connected by roads, as shown. A race uses each road exactly once. The race starts at $S$ and finishes at $Q$. How many possible routes are there for the race? <image1>
Answer: 6
Problem: <image>Question: Three equilateral triangles are cut from the corners of a large equilateral triangle to form an irregular hexagon, as shown in the diagram.
The perimeter of the large equilateral triangle is $60 \mathrm{~cm}$. The perimeter of the irregular hexagon is $40 \mathrm{~cm}$. What is the sum of the perimeters of the triangles that were cut from the large triangle?
<image1>
Choices:
A. $60 \mathrm{~cm}$
B. $66 \mathrm{~cm}$
C. $72 \mathrm{~cm}$
D. $75 \mathrm{~cm}$
E. $81 \mathrm{~cm}$
Answer: A
Problem: <image>Question: A $3 \mathrm{~cm}$ wide strip is grey on one side and white on the other. Maria folds the strip, so that it fits inside a rectangle of length $27 \mathrm{~cm}$, as shown. The grey trapeziums are identical. What is the length of the original strip?
<image1>
Choices:
A. $36 \mathrm{~cm}$
B. $48 \mathrm{~cm}$
C. $54 \mathrm{~cm}$
D. $57 \mathrm{~cm}$
E. $81 \mathrm{~cm}$
Answer: D
Problem: <image>Question: Seven standard dice are glued together to make the solid shown. The pairs of faces of the dice that are glued together have the same number of dots on them. How many dots are on the surface of the solid? <image1>
Answer: 105
Problem: <image>Question: Inside a square of area $36 \mathrm{~cm}^{2}$, there are shaded regions as shown. The total shaded area is $27 \mathrm{~cm}^{2}$. What is the value of $p+q+r+s$ ? <image1>
Choices:
A. $4 \mathrm{~cm}$
B. $6 \mathrm{~cm}$
C. $8 \mathrm{~cm}$
D. $9 \mathrm{~cm}$
E. $10 \mathrm{~cm}$
Answer: D
Problem: <image>Question: The cube shown is divided into 64 small cubes. Exactly one of the cubes is grey, as shown in the diagram. Two cubes are said to be 'neighbours' if they have a common face.
On the first day, the white neighbours of the grey cube are changed to grey. On the second day, the white neighbours of all the grey cubes are changed to grey.
How many grey cubes are there at the end of the second day? <image1>
Answer: 17
Problem: <image>Question: The diagram shows a pentagon. The lengths of the sides of the pentagon are given in the diagram.
Sepideh draws five circles with centres $A, B, C, D$ and $E$ such that the two circles with centres at the ends of a side of the pentagon touch on that side. Which point is the centre of the largest circle that she draws? <image1>
Choices:
A. $A$
B. $B$
C. $C$
D. $D$
E. $E$
Answer: A
Problem: <image>Question: Katie writes a different positive integer on the top face of each of the fourteen cubes in the pyramid shown.
The sum of the nine integers written on the cubes in the bottom layer is 50. The integer written on each of the cubes in the middle and top layers of the pyramid is equal to the sum of the integers on the four cubes
<image1>
underneath it. What is the greatest possible integer that she can write on the top cube?
Answer: 118
Problem: <image>Question: A $3 \times 3 \times 3$ cube is built from 15 black cubes and 12 white cubes. Five faces of the larger cube are shown.
<image1>
Which of the following is the sixth face of the larger cube?
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: A
Problem: <image>Question: The diagram shows two rectangles whose corresponding sides are parallel as shown. What is the difference between the lengths of the perimeters of the two rectangles? <image1>
Choices:
A. $12 \mathrm{~m}$
B. $16 \mathrm{~m}$
C. $20 \mathrm{~m}$
D. $22 \mathrm{~m}$
E. $24 \mathrm{~m}$
Answer: E
Problem: <image>Question: The diagram shows four overlapping hearts. The areas of the hearts are $1 \mathrm{~cm}^{2}, 4 \mathrm{~cm}^{2}, 9 \mathrm{~cm}^{2}$ and $16 \mathrm{~cm}^{2}$. What is the total shaded area? <image1>
Choices:
A. $9 \mathrm{~cm}^{2}$
B. $10 \mathrm{~cm}^{2}$
C. $11 \mathrm{~cm}^{2}$
D. $12 \mathrm{~cm}^{2}$
E. $13 \mathrm{~cm}^{2}$
Answer: B
Problem: <image>Question: Adam the Ant started at the left-hand end of a pole and crawled $\frac{2}{3}$ of its length. Benny the Beetle started at the right-hand end of the same pole and crawled $\frac{3}{4}$ of its length. What fraction of the length of the pole are Adam and Benny now apart?
<image1>
Choices:
A. $\frac{3}{8}$
B. $\frac{1}{12}$
C. $\frac{5}{7}$
D. $\frac{1}{2}$
E. $\frac{5}{12}$
Answer: E
Problem: <image>Question: Ellie wants to write a number in each box of the diagram shown. She has already written in two of the numbers. She wants the sum of all the numbers to be 35, the sum of the numbers in the first three boxes to be 22, and the sum of the numbers in the last three boxes to be 25. <image1> What is the product of the numbers she writes in the shaded boxes?
Answer: 63
Problem: <image>Question: Two segments, each $1 \mathrm{~cm}$ long, are marked on opposite sides of a square of side $8 \mathrm{~cm}$. The ends of the segments are joined as shown in the diagram. What is the total shaded area? <image1>
Choices:
A. $2 \mathrm{~cm}^{2}$
B. $4 \mathrm{~cm}^{2}$
C. $6.4 \mathrm{~cm}^{2}$
D. $8 \mathrm{~cm}^{2}$
E. $10 \mathrm{~cm}^{2}$
Answer: B
Problem: <image>Question: Ella wants to write a number into each cell of a $3 \times 3$ grid so that the sum of the numbers in any two cells that share an edge is the same. She has already written two numbers, as shown in the diagram.
When Ella has completed the grid, what will be the sum of all the
<image1>
numbers in the grid?
Answer: 22
Problem: <image>Question: Ten kangaroos stood in a line as shown in the diagram.
<image1>
At a particular moment, two kangaroos standing nose-to-nose exchanged places by jumping past each other. Each of the two kangaroos involved in an exchange continued to face the same way as it did before the exchange. This was repeated until no further exchanges were possible. How many exchanges were made?
Answer: 18
Problem: <image>Question: Anastasia's tablecloth has a regular pattern, as shown in the diagram. What percentage of her tablecloth is black? <image1>
Answer: 32
Problem: <image>Question: Stan had 125 small cubes. He glued some of them together to form a large cube with nine tunnels, each perpendicular to two opposite faces and passing through the cube, as shown in the diagram.
How many of the small cubes did he not use? <image1>
Answer: 39
Problem: <image>Question: Ellen wants to colour some of the cells of a $4 \times 4$ grid. She wants to do this so that each coloured cell shares at least one side with an uncoloured cell and each uncoloured cell shares at least one side with a coloured cell.
What is the largest number of cells she can colour?
<image1>
Answer: 12
Problem: <image>Question: The diagram shows a parallelogram $W X Y Z$ with area $S$. The diagonals of the parallelogram meet at the point $O$. The point $M$ is on the edge $Z Y$. The lines $W M$ and $Z X$ meet at $N$. The lines $M X$ and $W Y$ meet at $P$. The sum of the areas of triangles $W N Z$ and $X Y P$ is $\frac{1}{3} S$. What is the area of quadrilateral MNOP ?
<image1>
Choices:
A. $\frac{1}{6} S$
B. $\frac{1}{8} S$
C. $\frac{1}{10} S$
D. $\frac{1}{12} S$
E. $\frac{1}{14} S$
Answer: D
Problem: <image>Question: The faces of a cube are painted black, white or grey. Each face is only painted one colour and opposite faces are painted the same colour. Which of the following is a possible net for the cube?
<image1>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: B
Problem: <image>Question: The large rectangle shown is made up of nine identical rectangles whose longest sides are $10 \mathrm{~cm}$ long. What is the perimeter of the large rectangle? <image1>
Choices:
A. $40 \mathrm{~cm}$
B. $48 \mathrm{~cm}$
C. $76 \mathrm{~cm}$
D. $81 \mathrm{~cm}$
E. $90 \mathrm{~cm}$
Answer: C
Problem: <image>Question: The diagram shows a rectangle of size $7 \mathrm{~cm} \times 11 \mathrm{~cm}$ containing two circles that each touch three of the sides of the rectangle. What is the distance between the centres of the two circles?
<image1>
Choices:
A. $2 \mathrm{~cm}$
B. $2.5 \mathrm{~cm}$
C. $3 \mathrm{~cm}$
D. $3.5 \mathrm{~cm}$
E. $4 \mathrm{~cm}$
Answer: E
Problem: <image>Question: Square $A B C D$ has sides of length $3 \mathrm{~cm}$. The points $M$ and $N$ lie on $A D$ and $A B$ so that $C M$ and $C N$ split the square into three pieces of the same area. What is the length of $D M$ ? <image1>
Choices:
A. $0.5 \mathrm{~cm}$
B. $1 \mathrm{~cm}$
C. $1.5 \mathrm{~cm}$
D. $2 \mathrm{~cm}$
E. $2.5 \mathrm{~cm}$
Answer: D
Problem: <image>Question: Martha multiplied two 2-digit numbers correctly on a piece of paper. Then she scribbled out three digits as shown.
What is the sum of the three digits she scribbled out?
<image1>
Answer: 6
Problem: <image>Question: Valeriu draws a zig-zag line inside a rectangle, creating angles of $10^{\circ}, 14^{\circ}, 33^{\circ}$ and $26^{\circ}$ as shown. What is the size of the angle marked $\theta$ ? <image1>
Choices:
A. $11^{\circ}$
B. $12^{\circ}$
C. $16^{\circ}$
D. $17^{\circ}$
E. $33^{\circ}$
Answer: A
Problem: <image>Question: James wrote a different integer from 1 to 9 in each cell of a table. He then calculated the sum of the integers in each of the rows and in each of the columns of the table. Five of his answers were 12, 13, 15, 16 and 17, in some order. What was his sixth answer? <image1>
Answer: 17
Problem: <image>Question: The diagram shows a net of an unfolded rectangular box. What is the volume of the box (in $\mathrm{cm}^{3}$ )? <image1>
Answer: 80
Problem: <image>Question: Ruth and Sarah decide to have a race. Ruth runs around the perimeter of the pool shown in the diagram while Sarah swims lengths of the pool.
Ruth runs three times as fast as Sarah swims. Sarah swims six lengths of the pool in the same time Ruth runs around the pool five times. How wide is the pool?
<image1>
Choices:
A. $25 \mathrm{~m}$
B. $40 \mathrm{~m}$
C. $50 \mathrm{~m}$
D. $80 \mathrm{~m}$
E. $180 \mathrm{~m}$
Answer: B
Problem: <image>Question: Freda's flying club designed a flag of a flying dove on a square grid as shown.
The area of the dove is $192 \mathrm{~cm}^{2}$. All parts of the perimeter of the dove are either quarter-circles or straight lines. What are the dimensions of the flag?
<image1>
Choices:
A. $6 \mathrm{~cm} \times 4 \mathrm{~cm}$
B. $12 \mathrm{~cm} \times 8 \mathrm{~cm}$
C. $21 \mathrm{~cm} \times 14 \mathrm{~cm}$
D. $24 \mathrm{~cm} \times 16 \mathrm{~cm}$
E. $27 \mathrm{~cm} \times 18 \mathrm{~cm}$
Answer: D
Problem: <image>Question: Dominoes are said to be arranged correctly if, for each pair of adjacent dominoes, the numbers of spots on the adjacent ends are equal. Paul laid six dominoes in a line as shown in the diagram.
<image1>
He can make a move either by swapping the position of any two dominoes (without rotating either domino) or by rotating one domino. What is the smallest number of moves he needs to make to arrange all the dominoes correctly?
Answer: 3
Problem: <image>Question: Wendy wants to write a number in every cell on the border of a table.
In each cell, the number she writes is equal to the sum of the two numbers in the cells with which this cell shares an edge. Two of the numbers are given in the diagram.
What number should she write in the cell marked $x$ ?
<image1>
Answer: 7
Problem: <image>Question: In the isosceles triangle $A B C$, points $K$ and $L$ are marked on the equal sides $A B$ and $B C$ respectively so that $A K=K L=L B$ and $K B=A C$.
<image1>
What is the size of angle $A B C$ ?
Choices:
A. $36^{\circ}$
B. $38^{\circ}$
C. $40^{\circ}$
D. $42^{\circ}$
E. $44^{\circ}$
Answer: A
Problem: <image>Question: Which of the diagrams below cannot be drawn without lifting your pencil off the page and without drawing along the same line twice?
<image1>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: D
Problem: <image>Question: A large square is divided into smaller squares, as shown. What fraction of the large square is shaded grey? <image1>
Choices:
A. $\frac{2}{3}$
B. $\frac{2}{5}$
C. $\frac{4}{7}$
D. $\frac{4}{9}$
E. $\frac{5}{12}$
Answer: D
Problem: <image>Question: A four-digit integer is written on each of three pieces of paper and the pieces of paper are arranged so that three of the digits are covered, as shown. The sum of the three four-digit integers is 10126 . What are the covered digits? <image1>
Choices:
A. 5,6 and 7
B. 4,5 and 7
C. 4,6 and 7
D. 4, 5 and 6
E. 3,5 and 6
Answer: A
Problem: <image>Question: In the diagram, $P Q=P R=Q S$ and $\angle Q P R=20^{\circ}$. What is $\angle R Q S$ ? <image1>
Choices:
A. $50^{\circ}$
B. $60^{\circ}$
C. $65^{\circ}$
D. $70^{\circ}$
E. $75^{\circ}$
Answer: B
Problem: <image>Question: Which of the following $4 \times 4$ tiles cannot be formed by combining the two given pieces?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: E
Problem: <image>Question: Cathie folded a square sheet of paper in half twice and then cut it through the middle twice, as shown in the diagram, before unfolding it all. How many of the pieces that she obtained were squares? <image1>
Answer: 5
Problem: <image>Question: Some identical rectangles are drawn on the floor. A triangle of base $10 \mathrm{~cm}$ and height $6 \mathrm{~cm}$ is drawn over them, as shown, and the region inside the rectangles and outside the triangle is shaded. What is the area of the shaded region? <image1>
Choices:
A. $10 \mathrm{~cm}^{2}$
B. $12 \mathrm{~cm}^{2}$
C. $14 \mathrm{~cm}^{2}$
D. $15 \mathrm{~cm}^{2}$
E. $21 \mathrm{~cm}^{2}$
Answer: B
Problem: <image>Question: Natasha has many sticks of length 1 . Each stick is coloured blue, red, yellow or green. She wants to make a $3 \times 3$ grid, as shown, so that each $1 \times 1$ square in the grid has four sides of different colours. What is the smallest number of green sticks that she could use? <image1>
Answer: 5
Problem: <image>Question: The integers from 1 to $n$, inclusive, are equally spaced in order round a circle. The diameter through the position of the integer 7 also goes through the position of 23 , as shown. What is the value of $n$ ? <image1>
Answer: 32
Problem: <image>Question: Prab painted each of the eight circles in the diagram red, yellow or blue such that no two circles that are joined directly were painted the same colour. Which two circles must have been painted the same colour? <image1>
Choices:
A. 5 and 8
B. 1 and 6
C. 2 and 7
D. 4 and 5
E. 3 and 6
Answer: A
Problem: <image>Question: The diagram shows the square $W X Y Z$. The points $P, Q$ and $R$ are the midpoints of the sides $Z W, X Y$ and $Y Z$ respectively. What fraction of the square $W X Y Z$ is shaded? <image1>
Choices:
A. $\frac{3}{4}$
B. $\frac{5}{8}$
C. $\frac{1}{2}$
D. $\frac{7}{16}$
E. $\frac{3}{8}$
Answer: E
Problem: <image>Question: A large square is divided into smaller squares. In one of the smaller squares a diagonal is also drawn, as shown. What fraction of the large square is shaded? <image1>
Choices:
A. $\frac{4}{5}$
B. $\frac{3}{8}$
C. $\frac{4}{9}$
D. $\frac{1}{3}$
E. $\frac{1}{2}$
Answer: E
Problem: <image>Question: The diagram shows a shape made up of 36 identical small equilateral triangles. What is the smallest number of small triangles identical to these that could be added to the shape to turn it into a hexagon? <image1>
Answer: 18
Problem: <image>Question: Each cell of a $3 \times 3$ square has a number written in it. Unfortunately the numbers are not visible because they are covered in ink. However, the sum of the numbers in each row and the sum of the numbers in two of the columns are all known, as shown by the arrows on the diagram. What is the sum of the numbers in the third column? <image1>
Answer: 43
Problem: <image>Question: The shortest path from Atown to Cetown runs through Betown. The two signposts shown are set up at different places along this path. What distance is written on the broken sign? <image1>
Choices:
A. $1 \mathrm{~km}$
B. $3 \mathrm{~km}$
C. $4 \mathrm{~km}$
D. $5 \mathrm{~km}$
E. $9 \mathrm{~km}$
Answer: A
Problem: <image>Question: Sacha's garden has the shape shown. All the sides are either parallel or perpendicular to each other. Some of the dimensions are shown in the diagram. What is the length of the perimeter of Sacha's garden? <image1>
Answer: 24