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:
| m/n | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 2 | 1 | 18 | 62 | 278 | 1146 | 5706 | 28707 | 154587 | 843476 |
| 3 | 18 | 38 | 583 | 5337 | 55815 | 617658 | |||
| 4 | 62 | 583 | 5327 | 257773 | |||||
| 5 | 278 | 5337 | 257773 | ||||||
| 6 | 1146 | 55815 | |||||||
| 7 | 5706 | 617658 | |||||||
| 8 | 28707 | ||||||||
| 9 | 154587 | ||||||||
| 10 | 843476 |
Already computation of S(5,5) seems to be a very hard task on the basis of present knowledge.
Read more about this topic: Survo Puzzle
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