What is the 100th letter in the pattern ABCABCABC...?
I notice that the pattern repeats every three letters, so I can use modular arithmetic to find the position of the 100th letter within the cycle. If I divide 100 by 3, I get a quotient of 33 and a remainder of 1. This means that the 100th letter is the same as the first letter in the cycle, which is A. 