Beeby Finishes ultrahardcore 91

The Beeby series continues on trial wounded ultrahardcore 91 until the expanding coloring cluster can  take it home. Is your trial-less solution ready?

Next up t is  a 1-way from 1r6c3 that is exended back to 3r2c3 for a second removal from r3c3.  Or you can call it a boomer from 4r3c with wink into 1 to a wink into 3.







Another 1-way from 3r2c3 slinking into r2c5. The shortcut version slinks in (red) to green 8r2c5 from blue 7r5c9.

The boomer interpretation starts from green 8r2c5 and winks in to r2c3. On the removal, the boxline Nc6 picks off two more, including 3r5c6 that enables the green XY chain and boxline.


Then pick the interpretation for Beeby’s thing on the right: an ALS-18, a 148-wing, or a Bent Almost Restricted 3-set ( 3-BARN).

Back in ALS land, the long red one stretches out for an ALS_81,




then shortens up below for an  ALS_18, bringing with it  with a naked triple.


I’m watching for a cluster expansion. A new 8 slink was just added.  Although the cluster is not expanding, the increasing number of bv is a sign of progress.

Here is a bv style ALS_81, creating a clue, for




and the hidden unique rectangle at the left.

It then takes the AIC ANL





and the ALS_29 to the right,


and another hidden unique rectangle removing 8r3c7, to release  a coiled spring of cluster expansion.







The UR removal turns 8r1c7 green, trapping 1 and 3. The 3 trap brings clues in NE and r1, but let’s hold the clues and let the candidates spread the cluster. The 1r1c7 trap greens 1r1c2.

As the cluster spreads south, a SEc7 boxline removes 1r9c9, and 6r5c9 is removed by green or blue.








A timely XY ANL keeps it going,




as follow up clues and cluster expansion  bring trap after trap.


Coloring finishes the cluster, demonstrating one of the reasons why ultrahardcores are so hard. This one gets ever so close to having two opposing solutions.

The finish is the blue wrap traced here:





One more post on ultrahardcore 91, for you to compare Beeby’s ALS_XZ intensive path with the Sudokuwiki alternative.


So perhaps it’s time for a diagram for the next Stefan Heine ultrahardcore in the review, # 135.  If you didn’t order a copy, get it done. After the review, there will be 240 right page ultrahardcores left for you to do all by yourself, perhaps with your favorite solvers and your own uncoded discoveries. Maybe even one of my trials. You’re welcome.



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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