Seth and Cain play a game. They take turns, and on each turn a player chooses a pair of integers from 1 to 50. One integer in the pair must be twice the other, and the players cannot choose any integers used previously. The first player who is unable to choose such a pair loses the game.
If Seth starts there a winning strategy that relies on him picking one of two particular pairs of numbers on the first turn.
What are the four numbers that make up these two pairs.
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Maclaurin Mathematical Olympiad 2020 (2020)
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