English Day of Beijing Mathematics ClubPartⅠ: Questions 1 to 10, 10 marks each1.At the right is shown a 4 × 4 grid. We wish to fill in the grid such that each row, each column, and each 2 × 2 square outlined by the thick lines contains the digits 1 through 4. Some grids have already been filled in. Find the number of ways we can complete the rest of the grid.Answer： 2.The areas of the faces of a cuboid are 84 cm2, 70 cm2 and 30 cm2. Find the volume of the cuboid in cm3.Answer： 3.The fraction can be wrritten in the form where the greatest common divisor of m and n is 1, Find m+n. Answer： 4.Find the sum of all the integers N > 1 with the properties that the each prime factor of N is either 2, 3, 5 or 7, and N is not divisible by any perfect cube greater than 1.Answer： 5.A large fresh water reservoir has two types of drainage system, small pipes and large pipes. 6 large pipes, on their own, can drain the reservoir in 12 hours. 3 large pipes and 9 small pipes, at the same time, can drain the reservoir in 8 hours. How long will 5 small pipes, on their own, take to drain the reservoir?Answer： minutes6.At a local village gala, the entire population turned up, 500 people. The event raised £3,000. Tickets were priced as follows: £7.48 per man, £7.12 per woman and £0.45 per child. How many children were there?Answer： 7.Each of the distinct letters in the following addition problem represents a different digit. If A=4, find the number represented by the word “MEET”.Answer： 8.Let two 8×12 rectangles share a common corner and overlap. The distance from the bottom right corner of one rectangle to the intersection point along the right edge of that rectangle...
