The New Sudoku Players' Forum

[udosuk]

This topic has probably been addressed before, but sorry I couldn't find it.

I just want to know how many possible top bands are there for normalised solution grids (i.e. lexicographically minimal 81-digit strings). For example two of them are:

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123456789
456789123
789123456

123456789
457189236
689237145

Also, it would be nice to know the rough number of possible top two bands (i.e. r123456). We know the number of possible top three bands must be 5472730538.

Hopefully this can be found without using the complete catalog of solution grids.

[gsf]

This topic has probably been addressed before, but sorry I couldn't find it.

I just want to know how many possible top bands are there for normalised solution grids (i.e. lexicographically minimal 81-digit strings).

there are 416 row order minlex bands
these bands (labeled 001-416) do not appear as the first band of any row order minlex grid

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395 397 398 400 402 403 404 406 408 409 410 412 413 414 415

[udosuk]

Thanks heaps gsf!

It seems the thread which I should be studying is this one:

http://forum.enjoysudoku.com/viewtopic.php?t=5215

So there are 401 different top bands for minlex grids. A rather odd number!

Do you have statistics on how many different top 2 rows of all minlex grids?