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PUZZLE
HOW BAGSON BAGGED A BOARD GAME
Sidney Bagson was the twenty-fifth century’s world expert on ancient mathematical games. He was delighted when a French archeologist, on a dig in what had once been New Jersey, found an artifact that seemed to be the board of an unknown twentieth-century game. The board’s pattern is shown below. Somehow the artifact had survived the terri ble world war of the early twenty-first century that had virtually obliterated North America. Bagson had never seen such a board before. Try as he would, he was unable to deduce any reasonable playing rules. There was, however, a way to solve the mystery. The Weizmann Institute of Science, in Rehovot, Israel, where Bagson was a mathematician, owned a machine that en abled one to travel back in time and view past events. The machine and the person inside could not interact with the events being viewed. It had long been established that such interactions were impossible because they led to logical contradictions of the kind so thoroughly explored in primi tive science fiction. The Weizmann Institute gave Bagson permission to transport its machine to Secaucus, New Jersey, where the artifact had been unearthed. Extremely precise methods of quark dating established that the board had been made in the fall of 1987. Bagson climbed into the machine, adjusted the dials, and soon found himself watching a boy and girl playing the game. They were, of course, unaware of his presence. After observing a few dozen games it was easy to deduce the rules: 1. The game begins with a red counter on spot X, a blue counter on spot Y. Players choose colors, then alternate turns in moving their counter forward along the zigzag line. 2. On each move a player must advance his counter 1, 2, or 3 spots along the line. No jumps are allowed. 3. When the pieces meet—that is, when they are adjacent
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