1998 OIM Problems/Problem 1

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Problem

There are 98 points on a circle. María and José play alternately in the following way: each of them draws a segment joining two of the given points that have not been joined together previously. The game ends when all 98 points have been used as ends of a segment at least once. The winner is the person who makes the last stroke. If José starts the game, who can ensure victory?

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

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See also

https://www.oma.org.ar/enunciados/ibe13.htm