I was playing around with the 11.2 puzzle, not because I think I can solve it, but because it looks so cool - complete 4-arm symmetry of all the clues, and when I start drawing the links in I get symmetrical spaghetti
! The solution will have to have the same symmetry. Could this constraint be used to crack the puzzle manually?
The solver started by eliminating 3 from r1c7, but because of the symmetry of the clues it could just as well have started with 2<>r7c9, 1<>r9c3, or 4<>r3c1. In fact all of these eliminations can be made simultaneously using the same logic the solver gave for first step, just rotated 90 degrees around the grid. Every valid elimination, and every valid placement, will have this 4-fold property - it gives us sets of 4 propositions, each about a different digit and cell, that must either all be true or all be false. Specifically, any proposition about digit 1,2,3 or 4 must be true for 1,2,3 AND 4 (in their 90 degree shifted positions), or false for all of them. Any proposition about 6,7,8 or 9 must be true for 6,7,8 AND 9 (in their shifted positions), or false for all of them.
The b/b plot of this puzzle is very sparse, to say the least - no bival cells at all, and of the bilocs, no two digits have strong links ending in the same cell. I am guessing that the constraints from the symmetry will cause more interactions between cells, and interactions between digits, possibly offering some useful manually-discoverable chains. Anyone care to try it?
Is there agreed-on notation for sets of propositions which must be all true or all false together? Do they have a name? Are there sudoku theorems known about them?
I hope I'm not out in left field here--if I am, please laugh nicely
susume