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2024 SSMO Relay Round 3 Problems/Problem 3

Revision as of 16:02, 2 May 2025 by Pinkpig (talk | contribs) (Created page with "==Problem== Let <math>T = TNYWR-1.</math> Riley and Boris are playing a game on a <math>T\times T</math> grid of dots. The game alternates turns and starts with Riley. Each t...")
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Problem

Let $T = TNYWR-1.$ Riley and Boris are playing a game on a $T\times T$ grid of dots. The game alternates turns and starts with Riley. Each turn, a player draws a line connected two different random dots, exactly 1 unit apart. The first person to complete the first unit square loses the game. Given that Riley plays optimally and Boris plays randomly, the probability that Riley wins can be expressed as $P.$ Find the least positive integer $a$ such that $aP$ is an integer.

Solution

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