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?

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