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3 number game from 1 to 9999, 3 left to construct triangle, winning strategy

Source: Germany Federal - Bundeswettbewerb Mathematik 2010, round 1, p2

April 9, 2020
combinatoricsgamegame strategywinning strategy

Problem Statement

There are 99999999 rods with lengths 1,2,...,9998,99991, 2, ..., 9998, 9999. The players Anja and Bernd alternately remove one of the sticks, with Anja starting. The game ends when there are only three bars left. If from those three bars, a not degenerate triangle can be constructed then Anja wins, otherwise Bernd. Who has a winning strategy?
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