Z‐cyclic triplewhist tournaments—The noncompatible case, part I

Two odd primes $p_1 = 2^{b_1}u_1 + 1, p_2 = 2^{b_2}u_2 + 1, u_1, u_2$ odd, are said to be noncompatible if b 1 ≠ b 2 . For all noncompatible (ordered) pairs of primes ( p 1 , p 2 ) such that p i ≡ p i < 200, i = 1,2 we establish the existence of Z ‐cyclic triplewhist tournaments on3 p 1 p 2 + 1 players. It is believed that these results are the firstexamples of such tournaments, indeed the first examples of Z ‐cyclic whist tournaments for suchplayers. In Part 2 we extend the results of this study and establish the existence of Z ‐cyclictriplewhist tournaments on $3p_1^{alpha_1}p_2^{alpha_2} + 1$ players for allα 1 ≥ 1, α 2 ≥ 1 and p 1 , p 2 as described above. © 1997 John Wiley & Sons, Inc.