The football pool problem for 6 matches: A new upper bound obtained by simulated annealing

Abstract The set V3n of all n-tuples x = (x1, x2,…, xn) with xi ϵ {0, 1, 2} is considered. The problem mentioned in the title consists of determining σn, the minimal size of a subset W of V3n, such that for any element x in V3n there is at least one element y in W at a Hamming distance d(x, y) ⩽ 1. More popularly stated, σ6 is the minimum number of forecasts in a football pool of n matches, such that at least one forecast has at least n − 1 correct results. In this paper it is shown that σ6 ⩽ 74, which improves the previous best upper bound (σ6 ⩽ 79). This solution has been obtained by a computer search using the recently developed simulated annealing method.