Here are 8, 9 and 11 questions:
8.
There are 2016 different proper fractions. The sum of any 2015 of them is a proper fraction with denominator 2017 when expressed in its simplest form. Find the sum of these 2016 proper fractions.
9.
It is given that the sum of any 2 digits of a 3-digit number is equal to a multiple of the remaining digit. How many such 3-digit numbers are there?
11.
For positive integer n, denote 1 x 2 x 3 x ... x n = n!. If M = 1! x 2! x ... x 10!, find the number of positive factors of M whose are perfect cubes.
I hope you can see them.
uhm.... Sure you got that riddle right :E
