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Naked Subsets
Table of Contents
Naked Pair/Locked Pair
Naked Pair
Locked Pair
Naked Triple/Locked Triple
Naked Triple
Locked Triple
Naked Quadruple
How to find them
Naked Pair/Locked Pair
Naked Subsets are similar to Hidden Subsets, the only difference
is that it is not about candidates being confined to
cells (as in Hidden Subsets), but about cells containing only a
certain number of candidates.
Naked Pair
If you can find two cells, both in the same house, that have
only the same two candidates left, you can eliminate that
two candidates from all other cells in that house.
oKu: Solving Techniques - Naked Subsets (Naked Pair, Naked
Triple... http://hodoku.sourceforge.net/en/tech_n
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Left example: cells r8c3 and r8c4 are both in the same house
(row 8) and have both only candidates 3 and 9 left. It
follows immediately that on of the cells has to be 3 and the
other 9 (which is which is yet unknown). But we can safely
say that r8c2 can not be 3. The sudoku solves with singles after
that.
The example on the right shows a Naked Pair in a box: r4c5, r5c6
form a Naked Pair in box 5 thus eliminating
candidates 8 and 9 from all other cells in that box.
Locked Pair
If the two cells that form the Naked Pair are not only confined
to one but to two houses (a row and a block or a column
and a block), they are sometimes called a Locked Pair.
Candidates can be eliminated from both houses.
oKu: Solving Techniques - Naked Subsets (Naked Pair, Naked
Triple... http://hodoku.sourceforge.net/en/tech_n
12/3/2012
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Triple, Naked Quadruple, Locked Pair, Locked Triple)
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On the left side r3c79 is a Locked Pair in row 3 and block 3, it
therefore eliminates 2 from r3c3 (row 3) and from r1c9
(block 3). The right side shows a Locked Pair in row 8 and block
8 eliminating 18 candidates.
Naked Triple/Locked Triple
Naked Triple
oKu: Solving Techniques - Naked Subsets (Naked Pair, Naked
Triple... http://hodoku.sourceforge.net/en/tech_n
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Triple, Naked Quadruple, Locked Pair, Locked Triple)
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If you can find three cells, all in the same house, that have
only the same three candidates left, you can eliminate that
candidates from all other cells in that house. It is important
to note that not all cells must contain all three candidates,
but there must not be more than three candidates in the three
cells all together.
Left example: cells r2c2, r4c2, and r5c2 are all in the same
house (column 2) and together have only candidates 3, 6,
and 9 left. It follows immediately, that one of the cells has to
be 3, another 6, and the last 9 (which is which is yet
oKu: Solving Techniques - Naked Subsets (Naked Pair, Naked
Triple... http://hodoku.sourceforge.net/en/tech_n
12/3/2012
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Triple, Naked Quadruple, Locked Pair, Locked Triple)
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unknown). But we can safely say that r1c2 cannot be 6. The
sudoku solves with singles after that.
The example on the right shows a Naked Triple in a box: r3c45,
r1c5 form a Naked Triple in box 2 thus eliminating
candidates 1, 2, and 6 from all other cells in that box.
Locked Triple
If the three cells that form the Naked Triple are not only
confined to one but to two houses (a row and a block or a
column and a block), they are sometimes called a Locked Triple.
Candidates can be eliminated from both houses.
oKu: Solving Techniques - Naked Subsets (Naked Pair, Naked
Triple... http://hodoku.sourceforge.net/en/tech_n
12/3/2012
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Triple, Naked Quadruple, Locked Pair, Locked Triple)
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On the left side r789c5 is a Locked Triple in column 5 and block
8, it therefore eliminates 9 from r8c4 (block 8) and
from r2c5 (column 5). The right side shows a Locked Triple on 5,
6, 7 in row 5 and block 6 eliminating 18 candidates.
Naked Quadruple
Naked Quadruples work in exactly the same way as Naked Pairs and
Triples, just with four candidates in four cells.
Since an intersection between a row or column and a box can have
only three cells, a Locked Quadruple doesn't exist.
oKu: Solving Techniques - Naked Subsets (Naked Pair, Naked
Triple... http://hodoku.sourceforge.net/en/tech_n
12/3/2012
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Triple, Naked Quadruple, Locked Pair, Locked Triple)
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The left side shows a Naked Quadruple in row 8: candidates 3, 4,
8, 9 in cells r8c1346, eliminating 3 and 8 from r8c7
and 9 from r8c8. The right side has the Naked Quadruple in block
7: candidates 4, 6, 7, 9 in cells r8c2, r789c3.
How to find them
Finding Naked Subsets is best done, when all remaining
candidates have been penciled in. If that is the case, they are
oKu: Solving Techniques - Naked Subsets (Naked Pair, Naked
Triple... http://hodoku.sourceforge.net/en/tech_n
12/3/2012
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Triple, Naked Quadruple, Locked Pair, Locked Triple)
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rather easy to spot and very efficient.
Copyright 2008-12 by Bernhard Hobiger
All material on this page is licensed unde r the GNU
FDLv1.3.
oKu: Solving Techniques - Naked Subsets (Naked Pair, Naked
Triple... http://hodoku.sourceforge.net/en/tech_n
