(click here for rules)

Technique 5 :

The example shows that row number 1 and row number 5 both have a cell in the same column containing only the candidate numbers 4 and 7. These two numbers appear as candidates in all of the other open cells in that column too, but since they are the only two candidates in rows 1 and 5, these two numbers cannot appear anywhere else in the row, thus you can remove them. In the example, the two candidate pairs circled in red, are the sole candidates. Since 4 and 7 must be placed in either of these two cells, all of the pairs circled in blue, can remove those numbers as candidates. In this puzzle, this means 1 becomes sole candidate in the second row; 2 becomes sole candidate in row 6; and thus, 2 is sole candidate for row number 4.

You can also use this technique if you have more than two candidates. For example, let us say the pairs circled in red were instead triple candidates of the numbers 1, 4, 7. This would mean those three numbers would have to be placed in either rows 1, 2 or 5. We could remove these three numbers as candidates in any of the remaining cells in the column. This technique even works with four candidate numbers, assuming you have 4 possible candidates in four different cells in a row/column.

This is similar to Naked subset, but it affects the cells holding the candidates. In this example, we see that the numbers 5, 6, 7 can only be placed in cells 5 or 6 in the first column (marked in a red circle), and that the number 5 can only be inserted in cell number 8. Since 6 and 7 must be placed in one of the cells with a red circle, it follows that the number 5 has to be placed in cell number 8, and thus we can remove any other candidates for this cell; in this case, 2 and 3.

(click here for rules)

Technique 5 :

**Naked Subset**The example shows that row number 1 and row number 5 both have a cell in the same column containing only the candidate numbers 4 and 7. These two numbers appear as candidates in all of the other open cells in that column too, but since they are the only two candidates in rows 1 and 5, these two numbers cannot appear anywhere else in the row, thus you can remove them. In the example, the two candidate pairs circled in red, are the sole candidates. Since 4 and 7 must be placed in either of these two cells, all of the pairs circled in blue, can remove those numbers as candidates. In this puzzle, this means 1 becomes sole candidate in the second row; 2 becomes sole candidate in row 6; and thus, 2 is sole candidate for row number 4.

You can also use this technique if you have more than two candidates. For example, let us say the pairs circled in red were instead triple candidates of the numbers 1, 4, 7. This would mean those three numbers would have to be placed in either rows 1, 2 or 5. We could remove these three numbers as candidates in any of the remaining cells in the column. This technique even works with four candidate numbers, assuming you have 4 possible candidates in four different cells in a row/column.

**Hidden subset**(Example shown below is just part of the puzzle with that case)This is similar to Naked subset, but it affects the cells holding the candidates. In this example, we see that the numbers 5, 6, 7 can only be placed in cells 5 or 6 in the first column (marked in a red circle), and that the number 5 can only be inserted in cell number 8. Since 6 and 7 must be placed in one of the cells with a red circle, it follows that the number 5 has to be placed in cell number 8, and thus we can remove any other candidates for this cell; in this case, 2 and 3.

(click here for rules)

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