Definition of naked pair

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Definition of naked pair

Postby evert » Sun Nov 27, 2005 12:15 am

Does a naked pair consist of two numbers that can only be placed in two certain cells within a certain row/column/box?
Or does a naked pair consist of two cells within a certain row/column/box that can only contain two certain numbers?
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Postby Shazbot » Sun Nov 27, 2005 12:45 am

a NAKED pair is where two cells in the same row/column/box contain ONLY the same two candidates. These candidates may occur in OTHER cells in that group, but are the ONLY ones in those two cells. They may be removed from the other cells.

Example: 1 25 236 | 367 254 568 | 9 467 25
2 and 5 are the naked pair, and those numbers can be removed from all other cells (leaving a "naked single", 4, in column 5)

a HIDDEN pair is where two numbers can ONLY be placed in the same two cells in a row/column/box. There may be other candidates in those two cells, but those are the only places for those two numbers to go. The other candidates in those cells can be removed.

Example: 2347 4589 348 | 1 349 3459 | 48 2478 6
2 and 7 are a hidden pair, only able to be placed in the same two cells. All other candidates from those cells can be removed.


Check out Simple Sudoku for some great examples and explanations of these and many other sudoku techniques.
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Postby PaulIQ164 » Sun Nov 27, 2005 12:46 am

The... second is a naked pair. The first is a hidden pair.

I hope.
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Postby Pi » Sun Nov 27, 2005 10:46 am

No the first is naked and the second is hidden.

The naked pair allows you to remove the candidates of the naked pairs value from the rest of that row.

The hidden pair allows you to remove all candidates apart from the hidden pair from the boxes containing the hidden pair
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Postby evert » Sun Nov 27, 2005 5:04 pm

Suppose we have 5 empty cells in a certain row/column/box.

Then for each naked pair there is exactly 1 hidden triple.
And for each hidden pair there is exactly 1 naked triple.

I think this can be deduced logically from the definitions of naked/hidden n-tuple as I read them above.
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Postby emm » Sun Nov 27, 2005 7:42 pm

Pi - perhaps Paul was replying to the original post not the second:D

evert - yes, the triple is the flip side of the pair - the naked one exposes the hidden one (and vv)
Code: Select all
 | 27       25      257        | 6       8       1       | 34     34      9      |
 
 | 27       25      257        | 6       8       1       | 2345   3457    9      |

 | 237      2345    2457       | 6       8       1       | 34     34      9      |

   
 
emm
 
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