The ANL Test

A review of Paul Stephens’ books continues here with my discovery that his Nishio procedure,  when properly applied,  can be a practical X-panel analysis technique to uncover obscure grouped almost nice loops (ANL).  I propose calling it “the ANL test”.

Addicts 140 is an “extreme” puzzle from Paul Stephens’ The Sudoku Addict’s Workbook .  Paul’s note for this puzzle reads in part, ”Nishio is a controversial technique because it’s controlled trial-and-error.  However, it’s surprisingly easy …and can break puzzles which would otherwise need a complex Nice Loop inference chain.  The trick is to know where (and when) to look.”  The note ends with detailed hints for this puzzle.

Paul’s Nishio procedure is a two-sided coin. “Tails” is Nishio, the controlled T&E side of the controversy.  “Heads” is the ANL test that finds that “complex Nice Loop inference chain” (actually an almost nice grouped X-chain)  that Paul says you would otherwise need.

Addicts 140 6-wingMy sysudoku checkpoint for Addicts 140 agrees with Paul’s warning in the quote above.  After moderately hard basic solving, the bv scan and x-panels revealed one indecisive removal,  duplicated by a finned 6-wing and the  “short conjugate pair chain” (6-chain) that Paul predicted.

I found nothing else on the X-panel, and very little to go on in coloring. I marked the few AIC  hinges and a few of the compact ALS and explored some AIC chains, all with little promise.

In both Mastering Sudoku in 52 Weeks, and Addicts, Paul advocates Nishio when his limited repertoire of advanced solving techniques is exhausted.  On where to choose a guess candidate, his recommendation is to take one side of a bv.  When unsuccessful, Paul  just  keeps on  guessing.

The ANL test of the previous post follows the Nishio procedure after a trial candidate is chosen.  The last post illustrated that a successful Nishio that ends with a marked slink maps directly to the eliminating ANL removing the guessed candidate.  To avoid trial and error, we just get rid of the arbitrary choice of the trial candidate.  Sysudoku replaces such trials by filtered, comprehensive search.  A filter is a set of conditions that narrow the possibilities that are tested.

For analysis of the X-panel , I recommend noting, or perhaps marking, the slinks available for inference chains.  Grouping allows aligned candidates in a unit to form additional slinks.  The logical filter for grouped X-chain ANL is that the trial candidate have winks that are followed by slinks to a single candidate.

For Addicts 140, Paul’s hints for the Nishio leads directly to test the 9 in r6c6, a bv candidate on a well populated 9-panel.  Here is the filtered search that requires no hints.  The top left panel below shows the enumerated slinks afforded by grouping on this panel.  Five candidates are eligible.  The other panels show how the test procedure involves the grouped slinks.

Addicts 140 9-ANL analysis

On the X-panel template,  I can quickly copy a new panel and test each candidate.   In the panels above, the trial candidate is marked with “T” and its mark outs, with “t”.  Successive unit singles are marked with capital letters and their additional mark outs, with corresponding lower case letters.  The first two trials produce  Nishio failures and identical “naughty” loops with two alternation faults.  The next two also fail as Nishios, defining invalid patterns .  All four of these trials are finished when unit single A does not generate a new unit single.  Then when Nishio succeeds, in the bottom right panel, a removing ANL is pulled out of the tangle.

Addicts 140 ANL test removalHere are the results on the grid.

So Paul Stephens’ Nishio, which he admits to being trial-and-error, isn’t when it is applied in a smart search.  By filtering trial candidates and correctly interpreting the results, the procedure is converted into a method for finding difficult X-chain almost nice loops.  If the ALN test fails, no harm is done.  The two forcing chains advancing in lock step can only reach the Nishio contradiction when the trial candidate is removed by an X-chain ANL!  The logical secrets of the puzzle are not revealed by any guess.  The almost nice loop is one of those secrets, now revealed by goal centered analysis. If the test extends over all candidate units, it may have covered the correct pattern, but we don’t know that.

In the next post, I will forget about differences with Paul over solving instruction, and concentrate on what the “extreme” collection of puzzles in Weeks and Addicts  has to offer sysudokies.  I will also checkpoint a finish of Addicts 140 with the removal by our new ANL test.  Maybe you’d like to explore this first.

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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