5)Players A and B play the following game: a player writes, in a board, a positive integer n, after this they delete a number in the board and write a new number where can be:
i)The last number p, where the new number will be p−2k where k is greatest number such that p≥2k
ii) The last number p, where the new number will be 2p if p is even.
The players play alternately, a player win(s) if the new number is equal to 0 and player A starts.a)Which player has the winning strategy with n=40??
b)Which player has the winning strategy with n=2012?? number theorycombinatorics