LIM is not slim (Q2453490)

J. N. Silva introduced in 2002 the impartial combinatorial game of LIM played on three piles of token. A player takes \(n\) token from two piles but also adds \(n\) token to the third. In this paper, the authors introduce an equivalent rule-set LIM', a sort of coordinates transform, closely related to the classical game of NIM. Hence, a formula describing the \(\mathcal{G}\)-values of LIM is proved. It solves LIM completely. This short paper ends with an enumeration of the P-positions of LIM with \(n\) token and its relationship with Ulam-Warburton cellular automata.