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Naked Singles

The naked singles technique is a digit placement technique, meaning that it always allows you to place a digit in a cell. Simply stated, a cell is a naked single if there is only a single value that can possibly go in it. While this technique may seem simpler than the hidden singles technique, if you aren't using notes, naked singles can be harder to spot, because you need to realise that all other possibilities have been eliminated from that cell. Below is an example of this technique:

The cell highlighted in red must be an "8", because every other possible digit already shares a row, column or group with that cell. The digits which eliminate all the other candidates are marked in orage. This is an example of a Naked Single with Basis, meaning that the presence of the naked single is clear from the digits in shared groups. It is, however, possible to have a naked single which does not share a group with all other digits, as here:

In this case, the cell highlighted in red must be a "2", but it doesn't share a group with a "4", so you can't immediately determine that it is a naked single, unless you are keeping notes (which are of course present in the above picture). This is a Naked Single without Basis. If you weren't keeping notes, you would have to realise that the digit "4" cannot go in that cell, because of the following intersection reduction:

Which eliminates "4" as a candidate from the cells marked in red, including the cell which can then only be a "2". Hidden singles of both types (with and without basis) can be found trivially by keeping complete notes, but it can be more fun to find them without resorting to note-taking. Naked singles without basis can of course occur as the result of any candidate elimination technique, including all the more advanced techniques such as naked pairs and triples, hidden pairs and triples, aligned pairs, x-wings, y-wings and single and multi colours.

Once you have mastered the hidden singles, intersection reduction and naked singles techniques, you can solve all "Moderate" sudokus generated by Puzzle Tiger.

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