# Sudoku naked pair

By posting your answer, you agree to the privacy policy and terms of service. In the illustration below there is a naked triple indicated by the cells with a tan background.

The possibility of 4 in all five circled cells can be eliminated. Nude french milfs. Sudoku naked pair. In such a situation you are free to remove those candidates from cells in shared rows and columns.

All of these techniques are based on identifying all the possible "candidates" for a cell indicated by marks and then eliminating them one by one until only one possibility remains in a given cell. Notice one cell contains all three numbers while the other two cells only contain two. The red-highlighted 6 is a weak link to the yellow polarity of the chain. Obviously this can't solve all Sudoku puzzles.

As these two candidates exist nowhere else within the given nonet, they constitute a Hidden Pair and can be used to eliminate all other candidates from those two cells 4 and 5. Sudoku has only 9 items in a row. The 5 in this cell is called a "hidden single" because it can only be in this single location, and that fact is "hidden" by the presence of the other marks.

This situation can arise for one of two reasons. Big tits lust. A chain of bivalue cells containing the candidates 2 and 7 can be identified: This process, referred to as cross-hatchingis repeated for each row and each column.

Check it out for yourself that this is true. As these are the only candidates for those two cells, they cannot be candidates for other cells in the same row, column, or nonet. For the purpose of the example, they work fine 1,2, and 8 are only present in cells A B and C And the constraint you mentioned only applies to sudoku. The sheer numbers are daunting. I need to find out if there is a set of cells of size N in which a number of N candidates appear, where those N candidates are not present in any of the cells outside the set.

When there are exactly N candidates for N cells, then none of those candidates can be placed in a cell outside the set, because doing so would reduce the number of candidates for the set to less than N and the puzzle would be unsolvable. After this process, a naked single digit 8 appears in the fifth cell. But without the markup, the hidden pair is easier to see. It's really a very clever little idea, one of hundreds, I'm sure, that could involve almost-locked ranges.

Noting that 7 and 8 do not appear in the top center block but they are given as clues at the bottom of the 6 th column that leaves only 2 cells in the top center block where they could go, and so you have found the hidden pair.

In this example, the 2 and 3 in red on the right side is a naked pair. In this illustration with the candidate sets made explicit, it is much easier to spot the complimentary naked pair the 2s and 4s in the 1 st and 3 rd cells of the 6 th column in the block than the hidden pair. There is also some very helpful discussion of Sudoku techniques at BrainBashers. What are the values of the last two entries?

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The set of cells at the intersection of a row or column with a block is special because this set of cells has 12 buddies in common. Girls kissing pussy. However this seems horribly inefficient and I'd like to know if there is some algorithm that would help with this kind of thing.

For the purpose of the example, they work fine 1,2, and 8 are only present in cells A B and C And the constraint you mentioned only applies to sudoku. The sheer numbers are daunting. Go to list of all games. Sudoku naked pair. What we know is that there are N candidates for N cells. Any candidate k elsewhere that would do that may be eliminated. Nothing more than that. Notice in the image below how the number 2, 3, and 5 are the only candidates in their three respective cells.

Therefore these 3 digits must fall into these 3 cells although we do not know their exact positions yet. It is only necessary that the digit is not a candidate in any of the other cells in one of the intersecting regions.

Sets of three work similarly. Naked hot sister. Here we have one cell with two candidates. One simply needs to discern the n by n grid containing the set of candidate squares. Then these two digits can be safely eliminated as candidates in the other cells in blue of the same row. Analysis usually proceeds by identifying a set of cells usually 2 or 3 cells with the properties: This means that the empty cells of the naked pair now have only 1 candidate and that is not enough to populate both of the empty cells of the pair.

The four squares that contain the red numbers only contain numbers 2, 4, 8, and 9.

Subsets are not the only grouping that can be almost locked. On the left side rc5 is a Locked Triple in column 5 and block 8, it therefore eliminates 9 from r8c4 block 8 and from r2c5 column 5. I will give the definitions of naked and hidden triples and let you work out the rest. We don't care what's in the intersection. Check to see if we have either of the following two forcing conditions within any subset all of a specific candidate in a row, column, or block, or all the candidates of a given cell: If we had found sets of two, we could remove those from the graph.

When a candidate k is possible in only a single cell of a row, column, or block, then that cell must be k. Sexy naked twerk. To me it's a simple case of a conjugate pair working with two almost-locked ranges. Consider the configuration on the right.