Sixteen points are arranged in a 3 cm by 3 cm formation. Four of them are removed, leaving behind twelve points as shown in the diagram. If we choose three of these twelve points as vertices of a triangle, what is the largest possible area of this triangle, in cm² ?

The diagram below is the seating plan of a cinema. How many blocks of three adjacent seats are unshaded, not counting those in the first row ?

In an amusement park, each ride on the Bumper Cars costs 10 dollars, each ride on the Pirate Boat costs 15 dollars and each ride on the Roller Coaster costs 20 dollars. If Waldo spends 110 dollars in total on at least one ride of each kind, how many times has he taken a ride on the Roller Coaster ?

The first term of a sequence is 2. Each subsequent term is the remainder when 3 times the preceding term is divided by 5. Thus the second term is 1, the remainder when 3 x 2 = 6 is divided by 5. How many of the first 2015 terms of this sequence are equal to 1 ?

A cubic box of side length 15 cm has two holes. One of them is 5 cm above and 5 cm to the left of the bottom right corner of the front face. The other is 5 cm below and 5 cm to the left of the top right corner of the right face. The size of the holes and the thickness of the box are negligible. If the box is filled with water and one of its faces rests on a horizontal surface, some water will leak out through the holes. What is the maximum amount, in  cm³, of water that can remain inside the box ?

Goldie has two identical gold coins and Sylvia has three identical silver coins. They total weight of Goldie’s coins is equal to the total weight of Sylvia’s coins. If they trade one coin with each other, then the total weight of Goldie’s coins is 12 grams less than the total weight of Sylvia’s coins. What is the weight, in grams, of each gold coin ?

Jasmine tea sells for 320 dollars per kg while Oolong tea sells for 480 dollars per kg. A mixture consisting of 3 parts of Jasmine tea to 5 parts of Oolong tea sells for 450 dollars per kg. What is the maximum amount, in dollars, for which 10 kg of each of Jasmine tea and Oolong tea may be sold ?

Which of the following boxes has a net as shown in the diagram below ?

After the fourth test, Kenny’s average mark rise by 5 points, but after the fifth test, it drops by 9 points. If his total score in the last  two tests is 122 points, how many points does he score in the last test ?

Two paths are to be constructed in a garden 5m by 5m and three plans have been submitted. If the amount of space not taken up by the paths is to be as large as possible, which of the following statements is correct ?

City B is between City A and City C. William is riding a bike from B to C, a distance of 16 km. After he has gone 6 km, Mary begins to drive a car at 60 km per hour A to C. If William continues onward, he will reach C at the same time as Mary. If he turns back, he will reach B at the same time as Mary. What is his riding speed, in km per hour ?

The eight symbols 2, 0, 1, 5, I, M, A and S are to be arranged in a row. The digits must precede the letters, and 0 cannot be in the first place. How many such arrangements are there ?

A hotel has 11 rooms and each staff member has keys to 7 different rooms. For each room, at least two staff members must hold its key. What is the minimum number of staff members the hotel must have ?

A 10 cm by 18 cm piece of paper is folded twice into a 10 cm by 4.5 cm stack of thickness 4, as shown in Figure 1. Eight 1 cm by 3 cm holes, two of which are adjacent, are cut from the stack, as shown in Figure 2. When the stack is unfolded, as shown in Figure 3, what is the area, in cm², of this pieces of punctured paper ?

The diagram shows a 5 by 5 chessboard and an L-shaped piece which covers exactly 4 squares of the chessboard. It may be rotated or reflected. In how many ways can be it placed on the chessboard covering exactly 4 squares ?