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2 player game , with 1-100 - All-Russian MO 1997 Regional (R4) 9.2

Source:

September 23, 2024
number theorycombinatorics

Problem Statement

The numbers 1,2,3,...,10001, 2, 3, ..., 1000 are written on the board. Two people take turns erasing one number at a time. The game ends when two numbers remain on the board. If their sum is divisible by three, then the one who made the first move wins. if not, then his partner. Which one will win if played correctly?
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