Rearranging Digits

If we rearrange all digits of a three digit number from largest to smallest, we get ABC. Moreover, the original three digit number equals ABC - CBA. What is the original three digit number?

Grouping CMM Students

Dr. Hong is trying to group students in his meetup. If he forms groups of 2, one student is left out. If he forms groups of 3, one student is left out. If he forms groups of 4, one student is left out. If he forms groups of 5, one student is left out. If he forms groups of 6, how many students would be left out? 

Page Numbers in Leo's Diary

Leo plans to publish his diary. The pages of his diary book are numbered consecutively starting from 1. The digit 4 is printed 44 times on page numbers. What's the minimum number of pages his diary book can have?

Denominator

The fraction 360/N in the simplest form is a whole number. N is a positive integer. What is the total number of different values that N can be?