The Game of Timber

Richard J. Nowakowski1, Gabriel Renault2, Emily Lamoureux1, Stephanie Mellon1, Timothy Miller1
1Dalhousie University, Dept. Math. & Stats PO BOX 15000 Halifax, NS
2Univ. Bordeaux, LaBRI, UMR5800, F-33400 Talence, France CNRS, LaBRI, UMR5800, F-33400 Talence, France

Abstract

We analyze TIMBER, a game played on graphs. We find the \(\mathcal{P}\) positions for both normal and misère play on paths and show how to win the game. In passing, we also show a correspondence with Dyck paths, the Catalan, and Fine numbers. We present an algorithm for winning the Normal Play game on trees.