In this paper, we describe a new scoring problem for tournament environments, called tournament scoring problem. Unlike classical combinatorial problems with some initial state and constraints, the described problem is concerned with the construction of valid initial states according to some given final state and constraints. The problem can easily be generalised to incorporate various sports disciplines played in both tournament and league environments. Given a football tournament, this involves determining possible scores of all matches between teams, using the final state of the tournament table. We propose a constraint-based approach to a feasible solution of the problem for football tournaments, examining the subject of multi-parameter partition and introducing the notion of black&white graphs. Using some particular table data, experimental results are also presented along with the number of different scores and their computation time. (C) 2007 Elsevier Inc. All rights reserved.