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Chained Sets |
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A Chained Set is an Almost Linked Set (ALS) where the fin is the starting point of a Forcing Chain. If the forcing chain has a weak connection into any of the potential eliminations of the ALS, that candidate can be eliminated.
Consider the example on this page. The ALS is the 5 and 8 along the second row from the top. The 5 highlighted in blue is the fin of the ALS (if this value is false, then the hidden subset of 5 and 8 is true). This 5 is weakly connected to the 5 below, which is strongly connected to the 9 in the same cell, which is weakly connected to the 9 to the left, which is strongly connected to the 9 above, which is weakly connected to the 9 highlighted in green. Because this 9 is one of the values that would be eliminated if the ALS were a hidden subset, it can now be eliminated.
Consider the following logic. If the 5 in blue were false, then the hidden subset in yellow would be true eliminating all other candidates in those cells, including the 9. If, however, the 5 in blue were true, then the 5 below would be false, making that cell a 9, eliminating the 9 to the left, making the 9 above that true and eliminating the 9 in green. So we see that either way the 9 in green can be removed.
Note that the first connection out of the fin must be a weak connection, and that the connections must alternate between weak and strong.
Chained Sets are similar to Krakens, except that an ALS is used instead of a finned fish.
Sudoku Snake gives Chained Sets a skill value of 5000.
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