The Elimination of All but Two from a Tournament
J. G. Mauldon · IMA Journal of Applied Mathematics · 1973
In a tournament with N participants, the smallest number Q(N) of decisive matches which may be necessary for the identification of the runner-up has been observed by Schreier (1932) and Steinhaus (1950) to be the number M(N) defined in Section 1. Here we determine the smallest number P(N) of such matches which may be necessary for the identification of the top pair, champion and runner-up, without necessarily distinguishing the champion. In particular we show that P(N) = M(N)−1 if and only if N is of the form 2n+1, and that the optimal strategy has some unexpected features.