Trials

Sudoku players generally disdain an approach to solving which they refer to as “trial and error”.  It is repeatedly guess that a candidate is true, and following up the consequences of it being true. If that leads to a contradiction, the candidate is removed.  The practice is sure to reach a solution if it is accurately carried out long enough, but is considered without merit because it gains no knowledge of a logical solving path.

There is an alternative to simply abandoning a puzzle you can’t solve, which does employ Sudoku knowledge and skill to achieve a solution, and is not a compromise of your later attempt to solve the puzzle by purely logical means. Here we call it a trial.

A trial is the assembly of a set of candidates that are true or false together. The consequences of the set being true is followed up, either leading to the solution, or to a contradiction. Trials are designed to produce decisive information when it is a contradiction.

Trials are seldom based on coloring alone, but the trial of a cluster color is a good illustration of the trial concept. You assemble a cluster by carefully building a connected network of slinks. One color is entirely true and the other is entirely false. If you wanted, you could just decide to try the candidates of one color.  If you reach a contradiction, it will show that all candidates of that color are false, and all of the opposing color are true.  It’s a very easy, and likely decisive, form of trial. It’s not often applied, because if you have an decisive trial, you are very close to a having a completely logical solution by trap or wrap.

Two other forms of Sysudoku trial are described in the following pages. In the Single Alternate Sue de Coq,  a specific sequence of two or three candidates is tested. If true, that can be decisive enough to reach a solution. One advantage is you can calculate what you gain by a contradiction, before doing the trial.

A second type of Sysudoku trial is the pattern trial. Panels with sparse candidates along the edge, and crossing slinks limit the number of patterns that candidates of a value can form. Small pattern groups, and often single patterns, can be tested. Coloring can further limit the possible patterns, to make very decisive trials.