PaulIQ164 wrote:According to the solver I use (http://sudoku.sourceforge.net), the puzzle can't be solved any further without using trial and error (or at least, without using the 'Nishio' technique, which is essentially trial and error. Where did this puzzle come from?

Actually, that solver doesn't make the claim the puzzle *can't* be solved without trial and error, only that IT cannot do so. It all depends on what tactics are implemented. Pappocom considers puzzles that require swordfish in the T&E category.

Setting asided that you'll never be convinced that forcing chains aren't a little bit T&E, coloring isn't in the slightest. It may be misleading that Simes gave the *results* of the coloring tactic as a chain. The *results* of x-wing can also be written as a chain.

He could have described it this way:

- Code: Select all
` . . . | . 6 . | . 6 . `

. -6 . | . 6 . |+6 6 .

. . +6 | . . . | . . -6

--------+---------+--------

. +6 . | . . . |-6 . .

. . -6 |+6 . . | . . .

. . . | . . -6 | . +6 .

--------+---------+--------

. . . | . . +6 |-6 . .

. . . |-6 . . | . . +6

. . . | . . . | . . .

Pairs of cells are labled + or - if they are the only two in a group that can contain a 6. There is no particular chain required. No matter where you start, an exclusion will be made. In this case, there are two 6's with the same sign in column 7 [correction, thanks Pauliq164] -- they both can't be 6, so they both must NOT be 6. You can fill in ALL the "+" as sixes in one fell swoop.

Forcing chains are a proof, but coloring is a tactic to FIND a proof.