exponents of these numbers), only finitely many 3-smooth numbers can be winning openings, but it is not known whether any of them are. offered a $1000 prize for determining who wins in the first unsolved case, the opening move 16, as part of a set of prize problems also including Conway's 99-graph problem, the minimum spacing of Danzer sets, and the thrackle conjecture. References External links The Sylver Coinage Page Mathematical games Combinatorial game theory Recreational mathematics