coloin wrote:indeed this automorphic [how many ?] grid should have a name - as it cant be the MC grid ?

The original LS, with c1 = {123456789}, from which this puzzle was obtained is known as the "Back Circulant" LS, so I suggest that we call the Sudoku version the BC grid.

It has 54 Sudoku automorphisms. I have looked at some other grids with high-automorphism counts but can't find a "magic" case.

It does have 18C Sudoku puzzles (189 of them, all minimal). Here is one:

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`......789456...............23......1..789...............5...........234.91.......`

blue wrote:Have you scanned your LCT database for valid LS puzzles ... 19C in particular ?

I have scanned band 6 only, the largest (96 million grids). No 19C puzzle in the LCT catalog is a valid LS puzzle - but my conjecture is that, among the Sudoku grids, there are no 19-clue LS puzzles. So I didn't search any other bands.

To test this conjecture we would need an

Enum19C function. To find out whether any other grid has a 20-clue minimal LS/Sudoku puzzle we need an

Enum20C. (Are these extensions to the

BlueMagic suite feasible?)

Cheers

MM