The M-Wing Sudoku Technique Explained

Start with two matching bivalue cells

An M-Wing begins with two cells that each contain the same two candidates, such as heart and crescent. The cells do not need to see each other, and they usually sit in different parts of the grid. On their own, they do not form a naked pair because they may not share a row, column, or box. Their value comes from the fact that each cell has only two states. If the first cell is not a heart, it must be a crescent. If it is a heart, that choice can trigger a chain through another strong relationship. In Shapedoku, clean Notes make these matching bivalue cells easier to spot. Scan for repeated two-shape combinations, but verify that both cells truly have only those two candidates. A forgotten third candidate breaks the pattern before it begins.

Connect one candidate with a strong link

Choose one candidate from the matching pair, such as heart, and look for a strong link that connects the two sides. A common setup uses a conjugate pair: two heart candidates in one row, column, or box where one of them must be true. One end of that strong link must see the first bivalue cell, and the other end must see the second bivalue cell. Now follow the logic. If the first bivalue cell is heart, its nearby strong-link heart is false. The other end of the strong link must then be true, which removes heart from the second bivalue cell and forces that cell to crescent. If the first bivalue cell is not heart, it is already crescent. In both cases, at least one of the two bivalue cells contains crescent.

Remove the candidate seen by both endpoints

Once you know that one endpoint must contain crescent, any outside crescent candidate that sees both bivalue cells can be removed. The target might share a row with one endpoint and a box with the other, or use another combination of units. It only needs to see both. The elimination is narrow, so do not remove crescents merely because they lie near the chain. After making the removal, return to simpler techniques. One candidate deletion may create a naked single, hidden single, or locked pair nearby. M-Wings are most useful on Hard and Extreme puzzles after the obvious scans have ended. They are also a good bridge into longer chains because every step has a clear purpose: one bivalue choice, one strong link, one forced endpoint, and one shared target.

1. Find two bivalue cells containing the same candidate pair.
2. Choose one candidate from the pair to use as the linking candidate.
3. Find a strong link whose ends see the two bivalue cells.
4. Trace both states of the first bivalue cell and confirm that one endpoint must take the other candidate.
5. Remove that other candidate only from cells that see both endpoints.
6. Recheck every candidate and unit before applying the elimination.