To paint all the six faces of a $3\times3\times3$ cube, 6 g of red paint must be used. After the paint dries up, the cube is then cut into 27 identical unit cubes, as shown in the diagram below. Determine the amount of red paint, in g, that is needed to paint all the remaining unpainted faces of these unit cubes?
As shown in the diagram below, there is a $5\times7$ grid paper where each small square has an area of 1 cm$^2$. What is the total area, in cm$^2$, of the shaded regions?
In 1945, a famous mathematician said: “At a certain point in my life, the square of my age coincided with the year in which I was that age.” At what age did the mathematician made this comment?
How many different four-digit numbers (where its first digit cannot be 0) are there that can be formed by using two “2”s, one “0” and one “3” as its digits?
A $4\times6$ rectangle is constructed using six pieces, five of which are shown as the options. The sixth piece is a duplicate of one of them. Which piece appears twice?
The number 5009 has the following property: no matter how one re-arranges its digits, one cannot obtain a smaller 4-digit number which does not start with a 0. What is the next 4-digit number that has this property?
Alice and Bruce have the same number of tea bags, each of which may be used to make either 2 or 3 cups of tea. Alice uses all of her tea bags to make 41 cups of tea, while Bruce uses all of his tea bags to make 58 cups of tea. How many tea bags does each have initially?
A park has only linden and maple trees. At the start of the year, three fifths of the trees are maple trees. Some more linden trees are planted in the spring, and then only one fifth of all the trees are maple trees. In the fall, some more maple trees are planted, and once again, three fifths of all the trees are maple trees. Find the ratio of the number of trees now to their initial number.
A rectangle is dissected into six squares as shown in the diagram below. If the side length of the smallest square is 1 cm, what is the side length, in cm, of square A?
In the following addition:
$$\begin{array}{rrrrr}& & & N & O\\+&W&I&L&D\\\hline&T&E&E&N\end{array}$$
where different letters represent different digits and the same letter represents the same digit. If the letters N, W and T cannot be 0, then what is the minimum possible value of TEEN?
Andy has to pass through an underground maze. The enchantment on the maze requires Andy to pick up the piece of stone in the first room when he enters the maze. Then in each subsequent room he must exchange it with the next stone if that one is heavier.
The number in each room represents the weight of the stone in it, in kg. Andy can only walk to the right or down on the map. He also wants to carry as little weight as possible when he leaves the maze.
What is the least weight, in kg, he can leave with if he only walks right or down?
A Mathematics test consists of 3 problems, where each problem is being graded independently with integer points between 0 and 5. How many ways can the total points for this test be exactly 11?
In how many ways can we obtain a total score of 44 from the table shown, by following the conditions below?
- Start with any unit square of your choice and collect further different three numbers from the other squares which touch at least one selected square by a full side only.
- All the numbers chosen must be different and the number 12 must always be one of them.
The following figures below are two examples. Note that your answer must include both examples.
Answer: There are ______ ways, and the ways are as following:
[The source provides 20 copies of this blank answer board; one reusable copy is shown here.]
