Coloring LPO

We follow up the LPO attack on Maestro 22 in this post to illustrate how coloring enhances LPO pattern enumeration.

The clues from pattern 7a  yield

N8=>NEhs8=>NEr3np46=> NWr3np89=>Nr3np69, and E9m=>SE9m. 

The 5 patterns yield a 5-clue in E. The 2-panel then yields two 2-chains for two removals and  hidden single 2-clue.

Coloring the resulting grid shown here, starting with the NW naked pair (3,4), we can remove 3-candidates in Wc2, and r1c9.

With this much progress, we can expect  a substantial update in the LPO patterns.  In this update,  we need to repeat pattern enumeration.  This time, a freeform that incorporates a green or a blue candidate can continue only with candidates of that color, or candidates yet to be committed to either color. We use the colored grid to guide us, arriving at the freeforms below.

This time, we are saved from detailed pattern overlay. The coloring assisted LPO enumeration not only cuts the 1-patterns in half, it leaves two uncovered 1-candidates to be removed, and thereby generates 1-marks in W and a 1-clue in C.  The extended blue/green cluster then forces two green 3-candidates into c3, proving blue, and finishing Maestro 22.

Now for your checkpoint for line marking of Stuart’s Unsolveable of 1/29/12:

The trace goes

5f: r8, c8.  6f: r1, r2, r3, r5, r7, r8, r9.  7f:r4, r6. Close c1, c3, c4, c5, c6, c7, c9 .

Ugh! You know it’s bad news when line marking starts with a 5f.  Try to discover just how bad, up to and including coloring and AIC without ALS .  The next post will checkpoint you on all of that.

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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