MathDB

We say that a pile is a set of four or more nuts. Two persons play the following game. They start with one pile of

n \geq 4

nuts. During a move a player takes one of the piles that they have and split it into two nonempty sets (these sets are not necessarily piles, they can contain arbitrary number of nuts). If the player cannot move, he loses. For which values of

n

does the first player have a winning strategy?

Problem Statement