BALTIC-WAY 2000 Problem 10
- Answer
Two positive integers are written on the blackboard. Initially, one of them is 2000 and the other is smaller than 2000. If the arithmetic mean of the two numbers on the blackboard is an integer, the following operation is allowed: one of the two numbers is erased and replaced by . Prove that this operation cannot be performed more than ten times. Give an example where the operation can be performed ten times.
Dataset text NuminaMath olympiads. Quoted with source.
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