Home > Algebra, Combinatorics, Olympiad > IMC 2012 Problem 3

IMC 2012 Problem 3


Given an integer {n>1}, let {S_n} be the group of permutation of the numbers {1,2,..,n}. Two players {A} and {B} play the following game. Taking turns they select elements (one element at each time) from the group {S_n}. It is forbidden to select an element that has already been selected. The game ends when the selected elements generate the whole group {S_n}. The player who made the last move loses the game. The first move is made by {A}. Which player has a winning strategy?

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  1. GP
    July 30, 2012 at 8:09 am

    I don’t have a complete solution to this yet, but from the (small) examples I’ve taken, it seems like A has the winning strategy.

    • August 1, 2012 at 6:32 pm

      I’m don’t think that you are entirely right. For large n B has the winning strategy. I’ll post a solution soon.

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