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Naked Singles

The naked singles technique in Killer puzzles is an extension of the technique as used in regular Sudoku puzzles, which is discussed here in the Sudoku Solving Techniques section. Simply put, if all options have been eliminated from a cell except for one possibility, then we know that digit must go in the cell:

In the example above, the cell in red must be a "1", because the cell shares either a row or a column with every other digit (the digits which eliminate all other possibilities are highlighted in orange). In Killer puzzles, the same digit cannot appear twice in any cage, so if a cell shares a cage with a digit, then that digit cannot go in that cell, just as if it shared a row, column or box.

The above example is a Naked Single with Basis, meaning that digits already placed in the puzzle eliminate all other possibilities. This is not always the case, and in Killer puzzles, the other kind of naked single is far more common:

In this case, the cell highlighted in red must be an "8", because all other possibilities have been eliminated. The cell, however, only shares groups and cages with the digits "1", "3", "4", "7" and "9". However, because the cell's cage has a sum of 17, the cell must be either an "8" or a "9". Because the highlighted cell shares a column with a "9", it can only be an "8".

Copyright © Adam A. Brown, 2006, All Rights Reserved. www.sudokutiger.com