A Kampelmann Hard With Bypass Coloring


Ever have a Sudoku fail to tie down a solution? Hard 109 of last post seems to fail to do so without a trial. Coloring, which has found many multiple solutions, defines the unique solution for this one.

Starting with 4-fills, r2 has  no clue seeing two box cells.   But c2 places NW2 and leaves a 3-fill for later.

Then in c6, we get a 4-fill bonus. It’s not practical to look for naked singles in every cell, but as you check a 4-fill you already have five values seeing the four cells. Does any cell have three more? Three more see r1c8, but only  5 is absent from c6. Two absentees see r4c6, and two see r8c6, but r6c5 has three more!

Because unresolved 4-fills are so few in number, it’s worth it to scan their free cells for naked singles.

Now on your own or following the trace, the bypass continues:

Eventually you get a near BUG, but with two cells of three values. What is the solution? By trial, one works and one doesn’t.

Instead, we add coloring. Ignoring column 9, the cluster wraps green, with two green 9’s forced in r8.

The solution is the blue army, plus an uncolored 9r8c9.

Waiting for the next Washington Post 6-star, I went to the library and copied this USA Today Weekend 5-star. It’s almost bypassed by 2, 3 and 4-fills, and holds out through box marking. Well, almost.

Do the x-fills first. It’s the low hanging line marking fruit available in the bypass.

If you’re new, look in The Guide/Bypass for x-fill finding.

About Sudent

I'm John Welch, a retired engineering professor, father of 3 wonderful daughters and granddad to 7 fabulous grandchildren. Sudoku analysis and illustration is a great hobby and a healthy mental challenge.
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