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You can identify them yourself or load the puzzle up in the solver to see them. Figure 2 : Load Example or : From the Start Just to show that pairs don't have to be aligned on a row or column, in this group of pairs we have a [4,7] pair on H2 and J1which removes some 7s in the same box.

Two other Naked Pairs eliminate further candidates at this stage. Naked Triples A Naked Triple is slightly more complicated because it does not always imply three numbers each in three cells. 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. In row E, centre box, are the cells E4E5 and E6 containing [5,8,9], [5,8] and [5,9] respectively. In total, those three cells contain [5,8,9], so we have fixed those numbers in those cells - just not which way round they will be.

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This allows us to remove those numbers from the rest of the unit the Triple is aligned on - namely the row. There is no trickery in these Triples because the cells that form the triples are the last three unsolved cells in those columns - so they are bound to contain the three remaining values.

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Given that fact, we can clear out those values from each box containing a Naked Triple and only the box, since there is nothing to clear off in the columns. But the manoeuvre nets us a great deal of candidates and we get a solution of 9 in F8. Naked Quads A Naked Quad is rarer, especially in its full form, but is still useful if it 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 likely to be a Triple or Pair and the solver will highlight those first.

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It's a cluster of cells in box 1. A1B1B2 and C1 collectively contain [1,5,6,8], so those numbers must occupy those cells. That allows us to remove the yellow highlighted candidates. We don't consider higher orders of Naked candidates because there are only 9 cells in a unit.

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Same point arises with Hidden sets. It may be viable to look for such beasts in 12x12 or 16x16 Sudokus. Email addresses are never displayed, but they are required to confirm your comments. When you enter your name and email address, you'll be sent a link to confirm your comment. Monday Oct Please explain how to do this to enable easier solution making.

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Thank you. Janet D.

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Wednesday May So you won't need to look for "naked quin" if you do look for "hidden quads". Same for the "hidden quins" vs "naked quads". Andrew Stuart writes:. Appreciate the spelling correction, thanks. Tuesday 7-May Although i like most of the examples shown, The examples for the Naked Triples are not very useful.

Because the cells are align and it automatically exclude candidates. I don't call that a strategy. It is more simple elimination. We need to find examples where the cells are NOT align. Have a nice day. Friday Nov The first one I hit that it couldn't solve requires APE. I only point this out, because it is a lot easier to program when you're thinking in subsets. Wednesday Aug There is a Killer Sudoku board I would like you to look at Click on this link There will be a naked pair in b6,c7 linked by the cage starting at b6.

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That pair can eliminate candidates in b7. The solver seems not to see this. Thanks for this great example John.

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I have seen the gap in the search and plugged the omission. Good catch.

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Your example puzzle now completes. I have ated all solvers to 2. Thursday Jun In fact you can take this one step further; if you have checked for a Naked Quad and not found one, then you won't find a Hidden Quad unless all nine of the cells are still unfilled.

Wednesday Jul If two AB cells are located along an intersecting row and column, you can remove A and B from the intersection cell. This is because this cell will always "see" both A and B.

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This situation is easy to find if you first find conjugate pairs, then see if they are on a row and column that intersect at a cell having two or more candidates. Happens sometimes, not always.


Sunday Feb However, this does not effect the explanation. By what logic can you rule out the possibility of 1 being in A4 or A5 at this stage of the solution? If there are only two candidates left in two cells, they are compulsory.

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Thursday Sep Thursday Aug Merely that the cells contain 2 out of 3, 2 out of 3 and 3 out of 3 of the three numbers in the triple in column 1 and similarly for column 9. Saturday Jun Candidates can be eliminated from both houses. Sunday May I keep eliminating the wrong numbers. Thank you for the clear pictures and explanation.

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