Sudoku Assistant -- Solving Techniques - St. Olaf College

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The Sudoku Assistant uses several techniques to solve a Sudoku puzzle: cross-hatch scanning, row/column range checking, subset elimination, grid analysis,and what I'm calling 3D Medusa analysis, including bent naked subsets, almost-locked set analysis. Almost-locked set analysis can be extended to grids, where it forms the basis for all finned fish and sashimi, and also to what I am calling almost-locked ranges. When all that fails, the Sudoku Assistant resorts to hypothesis and proof and a sort of depth. All of these techniques are based on identifying all the possible "candidates" for a cell (indicated by marks) and then eliminating them one by one until only one possibility remains in a given cell.

Cross-Hatch Scanning (looking for singles)

The rule of singles requires:
When a candidate k is possible in only a single cell of a row, column, or block, then that cell must be k.
This situation can arise for one of two reasons. A naked single arises when there is only one possible candidate for a cell; a hidden single arises when there is only one possible cell for a candidate. Despite the name, hidden singles are far easier to find than naked singles. You should always start a Sudoku by finding all the hidden singles. No marks required!
XY-Wings. Just look for bent naked triples. Consider, for example, the board on the right. The 2 in row 8, column 1 can be excluded by the "bent triple" in rows 7 and 8.
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The dots in the cell in row 3, column 5, indicate that in that cell the numbers 4, 5, 6, and 8 are all possible. But in that top middle block only one cell can hold a 5. That's a hidden single. This is the most basic technique. Since a number can only appear once in any given column or row and must appear exactly once in any given 3x3 block, the easiest place to start is to first check for cells that must hold a value because no other cell in a 3x3 block can hold that number. For example, in this case the number 5 is excluded from all but one cell in the top center 3x3 block. The 5 in this cell is called a "hidden single" because it can only be in this single location, and that fact is "hidden" by the presence of the other marks. This process, referred to as cross-hatching, is repeated for each row and each column. Cross-hatch scanning is generally all that is necessary for "easy" puzzles. Most people do this step without actually making any marks.