Hi

Serg,

Thanks for considering it.

Mladen defined 'MinClues' for a (canonical) band, in terms of UA sets, and the size of the smallest set of cells that includes at least one cell from each UA set.

The number that's defined that way, would be the same, no matter how you transformed the band -- the UA sets would change, but the size of the smallest set, would remain constant.

An alternate way to define it, for a band that's part of a complete grid, is like this:

- Make a 54-clue puzzle, by clearing all of the cells in the band.
- Loop over clue counts ... N=0, N=1, etc.
- For each N, loop over all combinations of N clues from the original band.
- Stop as soon as you find a 54+N clue puzzle with a unique solution -- the original grid.

The N value, at that point, is the 'MinClues' number for the band.

If you did that for all 3 bands in a grid, and added the results, you would have one candidate of 4, for the grid's MCB number.

Doing the similar thing for the 3 stacks, 3 p-bands, and 3 p-stacks, would give the other 3 candidates.

The grid's MCB number, then, is defined to be the largest of the 4 candidates.

It is invariant with respect to grid transformations.

Using that method, would take an eternity for the full catalog of grids, so it would be better to approach the problem using select grid transformations, a band canonicalization routine, and a MinClues lookup table ... a "map", really ... mapping canonical bands to MinClues values.

My calculations for the catalog of standard sudoku grids, are running now.

With luck, the results will show similar anomalies, and any worries will be put to rest.

Update: Bad news ... for me, I guess ... no such luck.

Thanks Again,

Blue.