Let n be a positive integer, the players A and B play the following game: we have n balls with the numbers of 1,2,3,4,....,n this balls will be in two boxes with the symbols ∏ and ∑.
In your turn, the player can choose one ball and the player will put this ball in some box, in the final all the balls of the box ∏ are multiplied and we will get a number P, after this all the balls of the box ∑ are added up and we will get a number Q(if the box ∏ is empty P=1, if the box ∑ is empty Q=0).
The player(s) play alternately, player A starts, if P+Q is even player A wins, otherwise player B wins.a)If n=6, which player has the winning strategy???
b)If n=2012, which player has the winning strategy??? combinatoricsnumber theory