Question

Consider the subtraction game with the subtraction set (i.e. the number of chips each player can remove on a turn) of {1,2}. For which integers does the first ("next") player have a winning strategy? Argue for the correctness of your answer.

Answer 1

A move will comprises of expelling atleast one chip or greatest two chips. The last player who evacuates will win. Now consider the example. Suppose 1,2 chips are left. Then player who plays next will win. But on the off chance that it is 3 chips which are left back, at that point first player will win. Generalizing this further for whole numbers 0, 3,6,9,12,15, so on are on the whole wining positions for past player and rest for next player. P positions are those which are detachable by 3. So if n is splendidly distinguishable by n next player can win and in the event that n isn't separable by 3, at that point first player has opportunities to win.