It's Glen again. Last week , I mentioned how the relative difficulty levels of the ISL 2018 C4, C5 and C7 felt off to me. Out of curiosity, I looked up the C6 to see where it'd fit, and subsequently ended up solving it in the shower. (Yes, recurring theme, I know.) Anyway, this post will be about my thought process in solving this problem (sans paper, because shower). ( ISL 2018 C6 ) Let $a$ and $b$ be distinct positive integers. The following infinite process takes place on an initially empty board. If there is at least a pair of equal numbers on the board, we choose such a pair and increase one of its components by $a$ and the other by $b$. If no such pair exists, we write two times the number $0$. Prove that, no matter how we make the choices in (i), operation (ii) will be performed only finitely many times. Preliminary thoughts Here's a way of visualising this problem: we can think of representing our numbers as chips on a number line. Then, operation (i) corresponds to...
Comments
Post a Comment