^ J ^ ^ ^ ^ ^ ^ ^ i t i A of dining in the clubho se where each table seaged fouw people The question arose as to whether it would be pobsible to arrange the golfers at successive dinners so that everyone would have met everyone else exactly once after a suitable number of dinners The answer turned out to be 'Yes' and the drsired result can be achieved as foelows Suppose that, .or the first dinner, the golfers are arranged as follows:

It is well known that G. Tarry [1] was the first to publish a proof that the famous thirty-six officers problem posed by L. Euler [2] in 1779 has no solution but it appears to be less well known that he was the first to devise a systematic method of constructing bimagic and trimagic squares, that is, magic squares which remain magic when each entry is replaced by its square and, in the case of trimagic squares, also when each entry is replaced by its cube. Tarry's method was outlined in [3] and was explained and slightly improved upon in a book by E. Cazalas [4] published in Paris in 1934. Recently, there has been renewed interest in this topic.

In an earlier paper, [A.D. Keedwell, Australas J. Combin. 47 (2010), 227–238], we proved that complete sets of orthogonal diagonal Sudoku latin squares exist of all orders p 2 , where p is a prime. We also showed that complete sets of orthogonal Sudoku latin squares which are left semidiagonal exist of all orders p 2s , s> 1, and we conjectured that these may be right semi-diagonal also but we were not able to prove the latter result. In this note, we show that our conjecture regarding existence was correct.

We prove that complete sets of orthogonal diagonal Sudoku latin squares (sometimes called Sudoku frames) exist of all orders p(2), where p is a prime. We also show that complete sets of orthogonal Sudoku frames which are left semi-diagonal exist of all orders p(2s), 8 > 1. We conjecture that these may be right semi-diagonal also but we do not have a general proof. We show how these complete sets may be constructed.