The reason that I introduce forbidding chains at this time is quite simple:Īll the sudoku solving techniques, except perhaps those involving uniqueness of solution, fit Here is a brief key to terminology above: fc forbidding chain A = B A OR B, equivalent to A Union B A - B (not A) OR (not B), equivalent to A forbids B g8 shorthand for g8=number, in this case: g8=3 Using colors to deduce the possible eliminations. The term, coloring is derived from the common illustration of this technique In column g, the 3's are limited to two locations, g4 and g8. ![]() In this example, all the possible locations for 3's are highlighted by some sort of color. Many other techniques involving just one type of candidate can be placed under the tag, Xwings, Swordfish, Jellyfish, Finned Xwings, Finned Swordfish, Locked Candidates, and That is performed on just one type of candidate - or just one number, if you prefer. I also prefer to extend this idea to include any technique Amongst them are simple coloring, multi-coloring, colors. You can practice this strategy by installing the SudokuCoach application on your Android™ device.Get out the Crayola! Try and stay within the lines.ĭespite the childish name, this technique is VERY powerful. One of the two latters is the solution for its cell which eliminates candidate 5 in B1. ![]() In this example candidate 5 in B1 sees a blue candidate 5 in B6 and a pink candidate 5 in H1. SIMPLE COLORING (SEES TWO DIFFERENT COLORS) : as one color must be the solution, a candidate that "sees" (a Candidate "sees" another Candidate if both belong to the same region) two candidates of different colors is eliminated by one of them (we do not know yet by which one). If the yellow state is not the solution, then the green state is the solution. Hence no candidates colored in yellow can be the solution in their respective cells. If cells in yellow identified the solution then candidate 2 would be the solution in two cells of Row "D", which is not possible. In this example candidate 2 has twice the yellow color in Row "D". SIMPLE COLORING (TWICE IN A UNIT) : if two Nodes in the Chain belong to the same region (Row, Column or Square) and if they have the same color, then this color can not be the solution because a candidate can not be the solution for two cells in the same region all candidates with this color can be eliminated. Because there are only two possible states for a candidate, all candidates with the same color must simultaneously be the solution or can not be the solution. This strategy analyzes such chains and uses colors to display these states (hence its name). ![]() If we consider a longer Chain exclusively made of Strong Links, the successive Nodes alternate from one state to the other. This, in turn and for the same reason, implies that the candidate can not be the solution for the third Cell in the Chain.Ĭonversely if we assume that the candidate in the Cell at one end of the Chain is the solution for that Cell, then it can not be the solution for the middle Cell and it must be the solution in the other end Cell of the Chain. If we assume that the candidate in the Cell at one end of the Chain is not the solution for that Cell, then it must be the solution for the next Cell in the Chain because of the definition of a Strong Link. If two Strong Links share a common Cell, we can form a Chain of three Cells with the common Cell in the middle. Let us define a Strong Link as the relationship that exists between two Cells in a region (Row, Column or Square) when these two Cells are the only Cells in that region that contain a particular candidate: if the candidate is not the solution for the first Cell, it must be the solution for the second Cell, and vice-versa.
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