## Mashing the BUG

Bivalue Universal Grave, the uniqueness method, requires knowledge, or at least absolute faith, that the puzzle has a single solution.  Coloring is a powerful analysis tool for the near BUG situation, making such knowledge unnecessary.

A happy and prosperous New Year to my readers!

The BUG + 1 puzzle in the sudocue guide of November 2011 was suggested as a classic basic solving challenge for readers of the previous post.  Box marking of

1: NWt, Ct.  2: N2=>NWt.  3:NEm, Sm, SWm.  4: NWm.  5: Cm, NWt.  6: NEm, Sm.   7: C7=>(E7=>(NEm, E1m), E8m=>W8t).  8: N8=>N9m=>C9m.  9:

gets us only two clues, but line marking almost finishes the puzzle.  We get to the BUG + 1 lesson grid by marking only seven easy lines:

The trace is revised to my new 2D format, which leaves lists of effects of a single action together, either on a line, or going down the page without indenting.  Effects of an action follow on the next line, indented.  Multiple effects are separated by commas, and enclosed in parentheses.

Sudocue’s author “ruud” warns that the removal of the 1-candidate in r6c1 will leave us in BUG, where there are two solutions, or none.  Rejecting both possibilities as false, because we trust ruud for a single solution, the only course is to confirm the 1-candidate.

With less faith in a puzzle maker,  we should just rely on the logical properties of the Medusa cluster.

Coloring yields a decisive answer.  For clarity I have traced out a network of consistently colored cells.

Blue is discredited, by having two blue 1-candidates forced into W and r6. The green solution disposes of the r6c1 1-candidate’s rivals, and it take its place as the green 1 for W, r6 and c1. No trust required, and you know how easy this is.

The BUG + 1 example in  Stuart’s Logic of Sudoku does not work out so well. The slink marked version is shown here, without clues.

Andrew’s BUG + 1 uniqueness rule is to confirm the candidate that appears three times in its row, column, and box.

However, the consistently  colored BUG completed without this candidate reveals two solutions, a violation of the uniqueness condition for the rule.  Following the rule produces a solution, but it is the third solution.  Interestingly, the contradiction of the row and column color traps breaks cluster logic, and the third solution is a mix of blue and green candidates.  Shattered pottery does not hold water.