Hong Kong Maths Olympiad Heat Individual (95-96)

1.Find x if 4^x-3=8^x-2.

3.By considering n!=n×(n-1)×(n-2)×...×3×2×1, find the number of trailing zeros of 100!.

4.What is the largest integral value n that satisfies the inequality n²⁰⁰<5³⁰⁰?

5.A set of 110 stamps of the denominations of $0.1, $3, $5 worths $100 in total. Find the number of $3 stamps in the set of stamps.

6.For any value of m, the stragiht line y=mx+2m+2 passes through a fixed point P. Find the coordinates of P.

7.How many 3-digit numbers can be made from the figures 4, 5, 6, 7, 8, 9 when repetitions are allowed?

8.Express2.31313131... as a fraction.

9.If x and y are positive integers and x-y=5, find the least value of x²-y²+5.

10.Factorise x²(y-z)+y²(z-x)+z²(x-y).