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im playing:)

the player who made the 2nd last move

Well, duh. But is that player the first or the second to have originally chosen?

Ummm can they remove more than one element at a time?

its the player that goes 2nd who wins

Only one at a time @swissgirl
Show me a proof @dan815

|dw:1370241063380:dw|

|dw:1370241133384:dw|

sooo the first one loses!

|dw:1370241271520:dw|

so all even but +1 elements from s1=1 will give u an odd number of elements in total

I honestly have no idea what you're trying to do here.

it cant be that easy so.. i probably dont understand what a group of permutations mean xD

Hint 2: What are the orders of the maximal subgroups?

Would the size of s_n be nCn?

The size of \(S_n\) is \(n!\).