A stone is placed in a square of a chessboard with n rows and n columns. We can alternately undertake two operations:
(a) move the stone to a square that shares a common side with the square in which it stands;
(b) move it to a square sharing only one common vertex with the square in which it stands.In addition, we are required that the first step must be (b). Find all integers n such that the stone can go through a certain path visiting every square exactly once. combinatorics proposedcombinatorics