No 17‐player triplewhist tournament has nontrivial automorphisms

The existence of triplewhist tournaments for v players has recently been solved for all values of v except  = 17. For v  = 12 and v  = 13, a complete enumeration has shown the nonexistence of TWh ( v ), while constructions of TWh ( v ) have been presented for v  > 17. For several values of v , existence has been shown by constructing a TWh ( v ) with a prescribed, usually cyclic, automorphism group. In this article, it is shown that the strategy of constructing a TWh ( v ) with a prescribed automorphism group cannot succeed with TWh (17), since no 17‐player triplewhist tournament has nontrivial automorphisms. © 2004 Wiley Periodicals, Inc.