Plus and One-Sided Unique Polygons


In this post, the Gordon Guide’s Gordonian Polygons Plus and One-Sided Gordonian Polygons are shown to be variations of the unique polygon, defined here as a loop of cells, containing the same two numbers, which become a loop of conjugate pairs when extra candidates are removed. The name Unique Polygon, or UP, is proposed for all of these variations, since Peter Gordon’s Guide does not adequately defined it, or explain how it works.

gordon UP plusGordon’s example of the “Plus” variation does not require a remote pair to close the ring. Removal of both 4 and 6 from the “crown” cell r1c5 will result in two solutions at least, therefore 1 and 7 can be removed. The resulting 46 naked pair in c5 starts the collapse.

Gordon starts the one-sided polygon example with “You had to know it was coming.” Indeed, this is a variation already covered in the definition of my previous post.

gordon UP one sidedAgain, in the Guide’s “one-sided” example, a six member conjugate pair loop emerges if both 5’s are removed. This would guarantee at least two solutions, therefore the 5-group is true, removing 5r9c2 and triggering the collapse. You could also describe the uniqueness condition as imposing a box/line restriction.

This variation suggests we leave the “crown cell” out of the Unique Polygon definition, to include this variation. The UP is the “gem in the rubble” I mentioned earlier. Clearly, the extra candidates do not even have to be in the same side of the UP, for eliminations.

Also, let’s note that when “extra” guardian candidates are not confined to one crown cell, we may not find guardian candidates whose confirmation is required to avoid the removal of all UP extra candidates.

Next post, we show how the formation generally known as extended unique rectangles, but claimed by the Guide as “Gordonian”, is systematically revealed by Medusa coloring. The Gordon Guide provides the example, but as we will see, the Guide does not cover coloring, and actually invites confusion by using the term “coloring” for a trial-and-error method.

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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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