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 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.