Thread: November 2019
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Old 2019-11-28, 18:04   #80
yae9911's Avatar
Jul 2019

3110 Posts

To support the end stage of the challenge a bit, it certainly does not hurt to provide some more information. None of this is directly suited to solving the problem, but you can then classify how good your own results are.

Some time ago the question was discussed, which determinant values can be reached with Latin squares, which would not be permissible if the puzzle definition is interpreted restrictively. The few determinant values greater than 920000000 are the following ones: 920271375, 920606715, 921397680, 923005125, 923209245, 924220125, 926679285, 929587995. All were found by stupidly performing all possible 9! symbol permutations in the list of the 2393407 9x9 Latin squares listed with title "Isotopy classes with nontrivial groups" on Brendan Mc Kay's Latin Squares web page. This gives 1747706 distinct absolute determinant values, which is still not the full list. If you are patient and have fast web access, then you can download and view a 36 MB pdf file Occurrence Counts that gives you an idea of the distribution of determinants. Determinants > 900000000 are extremely rare.

The best determinant < 929587995 of a non-Latin square known to me is 927006660, found by Hermann Jurksch outside of the challenge. The record setting determinant value found in the challenge is > 933000000.

Last fiddled with by LaurV on 2019-11-29 at 02:41 Reason: added spoiler
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