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fluffpupkiki
fluffpupkiki
20.04.2021 • 
Mathematics

Subset take-away is a two player game involving a fixed finite set, A. Players alternately choose nonempty subsets of A with the conditions that a player may not choose: The whole set A, Or any set containing a set that was taken earlier (so if {2} was taken by player I, then all its supersets {2, } may not be taken next by player II). The first player who is unable to move loses the game. For example, if A is {1}, then there are no legal moves and the second player wins. If A is {1, 2}, then the only legal moves are {1} and {2}. Each is a good reply to the other, and so once again the second player wins. The first interesting case is when A has three elements. This time, if the first player picks a subset with one element, the second player picks the subset with the other two elements. If the first player picks a subset with two elements, the second player picks the subset whose sole member is the third element. Both cases produce positions equivalent to the starting position when A has two elements, and thus leads to a win for the second player. Verify that when A has four elements, the second player still has a winning strategy Can you make this precise, in terms of functions, sequences, simulate it?

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