Wex 426 Complex 1-Way, ALS_Wings, Cluster Bridge

These Weekly Extreme Competition posts were originally posted as they appeared in 2015. The analysis was  updated in 2023 with the added help of Phillip Beeby’s PhilsFolly solver, to replace trials.

In Basic, we get a naked quintuple which creates a Nc6 boxline.

After the boxline removals, corner pairs and a slink create a unique rectangle.

Regardless of extra candidates, 4r4c4 puts 5’s in two corners, and the slink puts 4’s in the other corners.

Two clusters can be started, but it takes a complex 1-way AIC to get the first ANL. Starting at 7r8c2, a true 7r8c5 erases the blue 7r6c5 to allow the 46 slink for the AIC. It’s not that the blue 7 is true. It’s only true if the starting 7r8c2 is false, and in that case the ending 7r3c3 is true. The removal happens regardless.

Complex chains require the extra work of looking ahead on  AIC building after identifying possible 1-way ANL victims.

Now comes a series of ALS-wings.

The first can be interpreted as an ALS XZ, but with a forcing chain connecting the X value sets. It’s also an ALS-wing, the Beeby label for a chain of 3 ALS, connected by value group winks. The victim sees a single in one ALS, and a matching value group in the other.

In the next ALS-wing the ALS in crossing lines, and the victim sees two end groups. Again the middle ALS happens to be a bv.

It looks hairier still, with a crossing line ALS in the middle, but the tough part is just identifying the ALS in the first place.

The ALS-wing series ends with a complex grouped 1-way, starting with 5r4c6  and a grouped 4 chain. Assuming the starting 5 is false, the 4 wink removes 4r4c3 to set up the ending terminal. The victim 5’s see the beginning and ending 5’s on of which is true.

A corner 5 then gets to be the fin in a Sashimi 5-wing.

We finally get some coloring action with an X-linked ANL makes a blue /green expansion.

Then the 4-chain grouped ANL removes 4r6c5, for a naked triple in the C box and in row 6.

The blue/green expansion from green 4r4c5 gives a trap in r5c3, and the a shortcut ANL on the right, is followed by the ANL on the left. The follow up bv support a third cluster.

The tan/yellow cluster resolves with two bridges. In c5 on 6:

not(green and yellow) =>

blue or tan.

In r8 on 5:

(not( blue and yellow) =>

green or tan.


(blue or tan) and (green or tan)

=>(blue or green) and tan => tan.

Now with tan NW5 comes

        green SW3, . .

           8r8c5, . . .

              8r9c9, orange) ,

and the Wex 426 solution

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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