Practice problem
Intro to Combinatorial Game Theory
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The Fifteen Game has two players, taking turns picking a number from 1 through 9 on each turn. Once a number has been picked, it cannot be picked again by either player. As soon as a player has a set of numbers which contain three distinct numbers that sum to exactly 15, that player wins and the game ends immediately.
Suppose that you go first and picked 7, your opponent picked 5, you then picked 4, and your opponent then picked 3. What is the next number that you should pick?