The arithmetic-periodicity of cut for C={1,2c}

is a class of partition games played on a finite number of finite piles of tokens. Each version of is specified by a cut-set . A legal move consists of selecting one of the piles and partitioning it into nonempty piles, where . No tokens are removed from the game. It turns out that the nim-set for any with is arithmetic-periodic, which answers an open question of Dailly et al. (2020). The key step is to show that there is a correspondence between the nim-sets of for and the nim-sets of for . The result easily extends to the case of , where .