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Found problems: 1

India EGMO 2022 TST, 2
Tags: wet , combinatorics
Let $a,b$ be arbitrary co-prime natural numbers. Alice writes the natural number $t < b$ on a blackboard. Every second she replaces the number on the blackboard, say $x$, with the smallest natural number in $\{x \pm a, x \pm b \}$ that she has not yet ever written. She keeps doing this as long as possible. Prove that this process goes on indefinitely and that Alice will write down every natural number. [i]~Pranjal Srivastava and Rohan Goyal[/i]