+586 1. How many three digit numbers are there such that the digits are non-zero, the tens digit is a multiple of the hundreds digit, the units digit is a multiple of the tens digit, and none of the digits are the same?
2. Find the number of positive integers \(n \le 1000\) such that \(15n\) is a perfect square.
1. The answer is 2*2*3 = 12.
2. The perfect squares from 1 to 1000 are 1, 4, 9, ..., 31^2. There are only two numbers that are multiples of 15, so the answer is 2.
