Let n ≥ 2 and k ≥ 2 be positive integers. A cat and a mouse are playing Wim, which is a stone removal game. The game starts with n stones and they take turns removing stones, with the cat going first. On each turn they are allowed to remove 1, 2, ⋯, or k stones, and the player who cannot remove any stones on their turn loses. \\\\ A raccoon finds Wim very boring and creates Wim 2, which is Wim but with the following additional rule: You cannot remove the same number of stones that your opponent removed on the previous turn. \\\\Find all values of k such that for every n, the cat has a winning strategy in Wim if and only if it has a winning strategy in Wim 2. OMCCcombinatoricswinning strategy