A Few More \(Z\)-Cyclic Whist Tournaments

\(Z\)-cyclic whist tournaments for \(q+1\) players, \({Wh}(q+1)\), where \(q\) is a prime, \(q \equiv 3 \pmod{4}\), are quite rare. Solutions for \(q = 3, 7, 11, 19, 23,\) and \(31\) were known in the early to mid 1890’s. Since that time no new such \({Wh}(q +1)\) have appeared.
Here we present \(Z\)-cyclic \({Wh}(q + 1)\) for \(q = 43, 47, 59\). Also presented for the first time is a \(Z\)-cyclic \({Wh}(45)\) and a \(Z\)-cyclic \({Wh}(40)\) that has the three person property. All of these results were obtained via the computer.