Pairs of students are looking at rows of pennies--laughing, talking, kidding one another about who is winning and who is making smart moves. The game, a simple game for two players, is One or Two?. The game begins with a player removing any one penny. Players then take turns, removing either a single penny or a pair of pennies from adjacent positions, until a player is able to take the last penny to win. At first, the students seem to think that winning is a matter of chance, but very quickly their play becomes strategic. This is no game of chance. Using logic, a player can cause her opponent to leave her the last penny! The game is fun, interactive, and logical--but are the students learning mathematics? This article answers that question, making a case for the use of logic games like One or Two? It describes the inclusion of a games project in a unit on mathematical logic as a context in which mathematical reasoning--from exploring to inquiring, from inquiring to making certain assertions, and from certainty to proving--can be taught and learned. The authors believe that the outcome of the project is sufficiently rigorous to legitimize the use of logic games for this purpose, and they present examples of students' writing to enable readers to judge for themselves. (Contains 6 figures.)