Ordered Tournaments and Ordered Triplewhist Tournaments with the Three Person Property R. J. R. Abel, 1 Gennian Ge 2 1 School of Mathematics and Statistics, University of New South Wales, N.S.W. 2052, Australia, E-mail: rjabel@unsw.edu.au 2 Department of Mathematics, Zhejiang University, Hangzhou 310027, Zhejiang, P. R. China, E-mail: gnge@zju.edu.cn Received August 18, 2007; revised January 15, 2008 Published online 3 March 2008 in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/jcd.20185 Abstract: It is well known that an ordered tournament OWh(v) exists if and only if v ≡ 1 (mod 4), v ≥ 5. An ordered triplewhist tournament on v players is said to have the three person property if no two games in the tournament have three common players. We briefly denote such a design as a 3POTWh(v). In this article, we show that a 3POTWh(v) exists whenever v> 17 and v ≡ 1 (mod 4) with few possible exceptions. We also show that an ordered whist tournament on v players with the three person property, denoted 3POWh(v), exists if and only if v ≡ 1 (mod 4), v ≥ 9. © 2008 Wiley Periodicals, Inc. J Combin Designs 17: 39–52, 2009 Keywords: whist tournament; 3POTWh; 3POTWh-frame AMS subject classifications: Primary 05B05 1. INTRODUCTION A whist tournament Wh(v) for v = 4n (or 4n + 1) is a schedule of games (a, b, c, d) where the unordered pairs {a,c}, {b,d } are called partners, the pairs {a, b}, {c, d}, {a, d}, {b, c} are called opponents, such that (1) the games are arranged into 4n - 1 (or 4n + 1) rounds, each of n games; Contract grant sponsor: National Natural Science Foundation of China; Contract grant number: 10771193; Contract grant sponsor: Program for New Century Excellent Talents in University. Journal of Combinatorial Designs © 2008 Wiley Periodicals, Inc. 39