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Hidden Double Loop |
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A hidden double loop is very similar to a naked double loop, except that whereas a naked double loop is based off of the concept of naked subsets, a hidden double loop is based off of the concept of hidden subsets. The Hidden Double Loop is a loop of paired candidates where two
cells at a time act as a node, and where the two values from each connection are the only values in the units. Then any candidate in those cells that is not part of the connections can be eliminated.
A practical example of a hidden double loop has not yet been discovered. For this purpose Sudoku Snake is offering a $20 reward for the first person to find an example where a hidden double loop is the next easiest solving technique in a sudoku puzzle that has a valid unique solution.
To help explain this technique, let's use the fabricated example on this page.
The hidden double loop is highlighted in yellow and the eliminations that come from it are highlighted in green in the image below.
Let's begin with the second column from the left. In this column there are four cells highlighted in yellow. The candidates 3 and 4 are ONLY found in these four cells. Now let's look at the top-left box. Only 4 of these cells are in yellow and the candidates 1 and 2 are ONLY found in these cells. Two of those cells also happen to be from our previous unit (the second column). Now in the second row from the top there are also four cells in yellow and the candidates 5 and 6 are only found in these cells, two of which are from our previous unit (the top-left box). If you follow this pattern around it holds true until we tie back into the second column again. Because each unit has 4 cells which exclusive contain 2 candidates, 2 of which pair into cells from units on opposite ends, this has become a hidden double loop. Be careful, there are many semblances and parts of hidden double loops out there. If any of the units has one of the two values in a cell that does not pair in to either side, or if the loop doesn't close back in on itself, it is not a hidden double loop.
You can follow the same logic for a hidden double loop as you can for a naked double loop. You need only consider hidden subsets instead of naked subsets. If you begin at any pair of linking cells and either pair of values, if neither, one, or both of the cells contains one of the two linking values, all the candidates below in green can be eliminated. This holds true for any starting point.
Sudoku Snake gives Hidden Double Loops a skill value of 2400.
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