Survo Puzzle - Open Survo Puzzles

Open Survo Puzzles

A Survo puzzle is called open, if merely marginal sums are given. Two open m × n puzzles are considered essentially different if one of them cannot converted to another by interchanging rows and columns or by transposing when m = n. In these puzzles the row and column sums are distinct. The number of essentially different and uniquely solvable m × n Survo puzzles is denoted by S(m,n).

Reijo Sund was the first to pay attention to enumeration of open Survo puzzles. He calculated S(3,3)=38 by studying all 9! = 362880 possible 3 × 3 tables by the standard combinatorial and data handling program modules of Survo. Thereafter Mustonen found S(3,4)=583 by starting from all possible partitions of marginal sums and by using the first solver program. Petteri Kaski computed S(4,4)=5327 by converting the task into an exact cover problem.

Mustonen made in Summer 2007 a new solver program which confirms the previous results. The following S(m,n) values have been determined by this new program:

Already computation of S(5,5) seems to be a very hard task on the basis of present knowledge.