Therefore one of the two yellow cells is a 7. That would violate the single answer rule. Though less common, this is a fun variation.Īssume in example 4 that neither of the yellow cells is a 7. Therefore the 1 and 6 can be removed as options from C7R4! One Sided Gordonian Rectangle Again, that would create 2 correct answers to the puzzle. Here is the theory … if the 4 digit option unsolved cell C7R4 is not a 5 or 9, then the options would be 1 and 6. Three of the cells have the same two digit options (1 and 6) and the fourth cell has the options 1 and 6 plus two other options (5 and 9). Please examine the four highlighted cells. Gordonian Rectangle PlusĮxample 3 is an actual puzzle in progress with the options for the unsolved cells printed at the top of those cells. Therefore the highlighted cell is a 4! Caution: This must happen within 2 boxes, not 4 boxes. We have already concluded above that we would be in a position of having two correct answers to the puzzle. Here is the theory … if the yellow highlighted cell is not a 4, then the options for the cell would be 1 and 2. Assume you are in the middle of a Sudoku puzzle and you find the situation similar to example 2 above (regardless if the blank cells are solved or not solved). The essence of the technique of Gordonian Rectangles and Polygons (and variations of both) is that the technique prevents you from getting into situations like example 1! This article will illustrate how to detect and implement this valuable technique! Gordonian Rectangles & Variations If you are in the middle of a puzzle or near completion and find a situation as you have in Example 1, you have made a mistake earlier in the puzzle! But wait, that would create 2 answers to the puzzle, which violates a rule of Sudoku. Both assumptions will complete the puzzle. Likewise, if we assume C5R5 = 3, then C5R6 =2, C8R5 = 2, and C8R6 = 3. If we start with cell C5R5 (column 5, row 5) and assume it to be a 2, then C5R6 = 3, C8R5 = 3, and C8R6 = 2. Also, we will assume the four unsolved cells have options “2” and “3”. ![]() ![]() Example 1 below illustrates the simplest essence of the technique.Īssume example 1 blank cells are solved cells for this puzzle. This is not a difficult technique, although some variations are a little tricky. Sudoku aficionado and puzzle book author Peter Gordon has been given credit for this technique, thus “Gordonian” has emerged. There is more than one name for this technique. This technique is all about ensuring that you arrive at a unique answer to a puzzle. One of the rules of Sudoku puzzles is there can be only one answer to a puzzle. This is perhaps the most important Sudoku solving technique that has ever been published! It cuts to the heart and soul of Sudoku puzzles. October 2015 – Step 2 - Part 3–Turbos & Interaction, by Dan LeKander.September 2015 – Step 1 - Part 2–Sudoku Pairs, Triplets and Quads by Dan LeKander.August 2015 – Introduction - Part I–Sudoku Puzzle Preparation for Dan’s steps 1-8
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