The New Sudoku Players' Forum

[enxio27]

Finished it! Once I got going with the GT chains and LT chains, it was just a matter of time. I think those chains are of far more importance (and interest) to these puzzles than the usual sudoku techniques. As a matter of fact, as far as standard sudoku techniques go, this puzzle requires nothing more difficult than locked candidates.

[Smythe Dakota]

.... there's no reason for not having ascending-chains across block boundaries ....

True. Furthermore, there's no reason not to have chains on the outside rims of the puzzles. One could know, for example, whether r6c1 is GT or LT its wrap-around neighbor at r6c9.

In fact, that would make the whole GTLT puzzle type more homogeneous than it is without those wrap-arounds. It would better retain some of the automorphisms present in vanilla Sudoku.

Bill Smythe

[Smythe Dakota]

.... True. Furthermore, there's no reason not to have chains on the outside rims of the puzzles. One could know, for example, whether r6c1 is GT or LT its wrap-around neighbor at r6c9. ....

Define a complete GTLT grid as one that has GT and LT signs on all cell boundaries, including those on box borders, and also including the wrap-arounds. Such a grid would always have exactly 81 GTLT signs.

Obviously, by adding extra GTLT signs to any valid (one-solution) puzzle, you would create a complete grid with only one solution.

Or, by making sure one of those extra signs is wrong, you could create one with no solutions.

So, what is the largest number of solutions any complete GTLT grid could have?

Bill Smythe