... by: Richard
Simple typo in "Naked Quads"In text to the left of grid Second A1 should be C1
Andrew Stuart writes:
Thanks! typo alerts always appreciated!






Naked Candidates 'Naked' in this context refers to all the remaining possible candidates on a cell which are going to be used in a strategy. The simplest such situation is a Naked Single  or the last remaining candidate on a cell. Generally speaking, if you are making notes on a Sudoku board you have reached a point where simple scanning of the rows, columns and boxes has brought you no further solutions. But you will be finding plenty of Singles on the easier puzzles, and hopefully not too few on the hardest ones. A Naked Single is exactly equivalent to saying "Ah Ha! Looking at that cell I can see every other number either in the same box, the same row or the same columns, it's the only number that can fit" Hidden candidates, mentioned below with regard to Pairs and so on, also have a Hidden Single Equivalent. It occurs when you find a cell with lots of possible but you reason "well, X can't go anywhere else in either the row, column or box, so it must go here. Naked Pairs A Naked Pair (also known as a Conjugate Pair) is a set of two candidate numbers sited in two cells that belong to at least one unit in common. That is they reside in the same row, box or column. It is clear that the solution will contain those values in those two cells and all other candidates with those numbers can be removed from whatever unit(s) they have in common.
A Naked Triple is slightly more complicated because it does not always imply three numbers each in three cells. Any group of three cells in the same unit that contain IN TOTAL three candidates is a Naked Triple. Each cell can have two or three numbers, as long as in combination all three cells have only three numbers. When this happens, the three candidates can be removed from all other cells in the same unit. The combinations of candidates for a Naked Triple will be one of the following: (123) (123) (123)  {3/3/3} (in terms of candidates per cell) (123) (123) (12)  {3/3/2} (or some combination thereof) (123) (12) (23)  {3/2/2/} (12) (23) (13)  {2/2/2} The last case is interesting and the advanced strategy XYWings uses this formation.
A Naked Quad is rarer, especially in its full form but still useful if they can be spotted. The same logic from Naked Triples applies, but the reason it is so rare is because if a Quad is present the remaining cells are more like to be a Triple or Pair and the solver will highlight those first.

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