Unsolvable 40 Logically Solved

In this post we checkpoint the solution of Stuart’s Unsolvable 40, via LPO and a coloring cluster extended by pattern slinks.  The solution of this puzzle by pattern analysis expresses well the ideals of Systematic Sudoku, and demonstrates what can be missed when a trial and error method is accepted as a solving method.

The previous post saw the extension of a coloring cluster by means of a strong link induced by pattern enumeration.  The extended cluster trapped a candidate of a previous red/orange cluster, proving its orange candidates false.

The elimination of the orange 7 invokes the  marking:

!7df=>red=> (r1np13=>NW4=>NE2=>(E2=>W2, r1np59), Wnp78=>purple = blue => pink = green, !1a) . 

The merger of the purple/pink and blue/green clusters springs several color traps, extending the blue/green cluster further.

The extended cluster forces two green 3-candidates in c7, proving blue true.  This is enough to  force the complete solution below with the marking:

Blue => (SE1=>SW1, Nr2np25, SW4=>SW3, E3, E4=>SE4=>(S4=>S6=>(C6=>C5=>E5=>E1=>W1=>W3, C3=>C4), SE3), S2=>(SW2, N2=>N5, S3).

Stuart’s Unsolvable 40 illustrates the ideals of Systematic Sudoku in many ways.  As expected,  it resisted the basic and advanced techniques preceding LPO in the SSOB, to  a point where many solvers turn to some form of trial and error.

The earlier trials on the blue/green cluster revealed  the solution, but we continued on.  As a result, we were able to illustrate how to add number pattern sets by tallies, and we discovered a new solving resource in patterns,  the pattern slink.

These results demonstrate the primary Systematic Sudoku argument against the use of trial and error in any form as a solving method.  The success of the trial hides the logical constraints that systematic solving seeks to reveal.

In this regard, we make no distinction between the trial of a cluster color constructed with diligent effort, and the trial of a candidate in an arbitrarily chosen bv cell.


Is there any occasion when T & E is justified?  Yes.  When a solution is not available, sysudokies might rely on such trials to obtain one, when the choice involved is narrowed sufficiently.  Human solvers make mistakes, and a solution is necessary for finding where a mistake reveals itself by removing a candidate in the solution. 

In this case I had not discovered how to obtain a solution from Andrew Stuart’s site (revealed soon), and I needed one.   My mistake was the omission of a freeform in pattern enumeration.  In the narrowed choice of the trials, both sides were wrong, so I knew for sure that a mistake had been made, and I found it in the most likely place, the very complex pattern enumeration. With the mistake corrected,  we then press on,  not accepting the corrected trial, decisive as it was, as a solving method.


About Sudent

My real name is John Welch. I'm a happily married, retired professor (computer engineering), timeshare traveling, marathon running father of 3 wonderful daughters and granddad to 7 fabulous grandchildren. The blog is about Sudoku solving. It covers how to start, basic solving to find candidates efficiently, and advanced solving methods in an efficient order of battle. It is about human solving methods, not computer solving.
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