The diagram below shows two different patterns that were formed by using the same set of shapes, in the same numbers, without overlaps. (Note: If one shape matches another shape after rotations or reflections, then they are viewed as the same shape.)
Which pattern from options (A)–(E) uses the same set of shapes, in the same numbers, as the following diagram?
A tour company offers two types of bus: a 26-seater or a 39-seater passenger bus. A group consisting of 212 tourists wants to use the buses provided by this company. If the company wants to optimize the selection of the buses so that the total number of empty seats is as small as possible, what is the smallest possible number of empty seats?
A recurring decimal is a decimal representation of a number whose digits are periodic in nature, meaning that, after some places, the same sequence of digits repeats continuously. For example, $\frac{1234}{9999}=0.12341234\ldots=0.\overline{1234}$. It is known that the recurring decimal of $\frac1{17}$ is 16 digits long. What is the sum of all the digits of the recurring decimal of $\frac1{17}$?
A polyhedra is a three-dimensional solid with flat faces, straight edges and vertices. Models of polyhedra are made from flat diagrams drawn on a board. On the diagram the faces are all connected, and one makes a model of it by folding the board along the lines of the diagram. A regular tetrahedron has two different diagrams as shown below:
Which diagram from options (A)–(E) is NOT a flat diagram of a cube?
A triangle has an area of 120 cm$^2$. If its base is increased by 50% and its height is decreased by 25%, then what will be the area, in cm$^2$, of the new triangle?
Five students are assigned to clean a classroom, where each student has the same efficiency work rate. One hour after they started, two of the students left for a scheduled singing practice. After two more hours, one of the remaining students left for a scheduled basketball practice. If the remaining two students completed the rest of the job in 1 hour, how long would it take for them to finish cleaning if all five students have stayed from the beginning?
A machine transmits messages that consist only of the letters A, B, C, D and E. Before the machine sends a message, A is encoded as 11, B as 10, C as 011, D as 010 and E as 00. For example, the message CABDE is encoded as 011111001000. If this machine sent 100111010111100010, what was the message?
The sum of the ages of Ann, Bob, Chris and Dan is 50. For each pair of them, the sum of their ages is at least 21. What is the minimum age that Ann can have? (Note: all ages are expressed as integer values.)
Select four pieces of $2\times2$ grid (which are labelled as A, B, C, D, E and F) and place them in the $4\times4$ grid such that the sum of numbers in each row equals the number written in the right-most side of each corresponding row and the sum of numbers in each column equals the number written in the bottom-most of each corresponding column. (Note: it is NOT allowed to rotate or reflect any of the $2\times2$ grids.)
Which of the following options is a correct solution?
Select six different digits from 0, 1, 2, 3, 4, 5, 7, 8 and 9, and then use these digits to create two positive three-digit numbers. What is the smallest possible positive difference (subtract the smaller number from the larger number) for these two three-digit numbers?
Let $N$ be a positive integer so that $N\times N=\underbrace{44\ldots4}_{2025\text{ digits}}\underbrace{88\ldots8}_{2024\text{ digits}}9$. What is the value of $N$?
Two squares, with sides 12 cm and 15 cm, are placed side by side, without overlapping, as shown in the diagram below. What is the area, in cm$^2$, of the shaded triangle?
The ladybug which is located on the left of the diagram wants to meet up with her friend located on the right. To get there, she will have to cross a field which consists of four kinds of flowers. Each kind of flower represents a different direction: either up, down, left or right. The black rectangles are deep pits that must be avoided.
It is known that there is a single path so that the ladybug can meet her friend. From options (A)–(E), which direction represented by the flower is correct?
A shipping company offers three different sizes of shipping boxes: Size A: $12\text{ m}\times9\text{ m}\times6\text{ m}$; Size B: $15\text{ m}\times12\text{ m}\times8\text{ m}$; Size C: $18\text{ m}\times10\text{ m}\times9\text{ m}$. Suppose that the $r$ pieces of Size A have the same total volume as $s$ pieces of Size B, which also have the same total volume as $t$ pieces of Size C. What is the minimum value of $r+s+t$?
Select an even number of distinct integers from the set $\{1,2,\ldots,n\}$ and group them into pairs. For each pair, find the positive difference of the two values (subtract the smaller number from the larger number), and then take the product of all such differences. If this product is equal to 2025, what is the least possible value of $n$?
A square is partitioned by segments into 9 regions so that the area of region I is equal to the total area of regions A, C, E and G, as shown in the diagram below, where the lengths of the indicated segments are shown. If the area of the square is 350 cm$^2$, what is the area, in cm$^2$, of the triangle formed by regions C, D and E?
