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Let's Make Number Place (Elementary course)
Strategy Guide
Number Place Strategy Guide
Naked Triple
When the same three numbers can only be inserted in three places within the same vertical line, horizontal line, and block (altogether called a group), any other squares within the same group cannot be those numbers.
Example 1
Pay attention to the three blue squares in the upper left block. Since numbers 1-6 cannot go into any of these three blocks, the three blue blocks must be 7, 8, or 9.
Since these three blocks must be 7, 8, or 9, the other empty squares in the block (marked purple) may safely be considered not 7, 8, or 9.
Confirming With Memo Numbers
Let's look at the example again using memo numbers.
The only numbers left in the three blue squares are 7, 8, and 9.
Since there are only three numbers AND only three squares, each square must be one of the numbers 7, 8, or 9. Since a number can only be entered once per 3 x 3 block, the numbers 7, 8, and 9 cannot go into--and therefore can be safely deleted from--the possible candidates for the remaining squares in the block.
Using this method you can remove quite a few candidates from the board.
In the next image we've add the red numbers 7 and 8.
Though the blue squares each have 7, 8, and 9, each square has different possible candidates of (7, 9), (8, 9), and (7, 8, 9).
However, the fact remains that one each of these squares must be 7, 8, or 9, and therefore 7, 8, and 9 may be removed from the possible candidates of the other squares in the block.
When you have only three possible candidates in three squares, you've got a naked triple.
Example 2
This time pay attention to the horizontal line at the top of the board. Which numbers can go into the blue squares?
Again, the only possible candidates for the blue squares are 7, 8, and 9. Since there are only three spaces and only three candidates, the blue squares must be 7, 8, or 9.
Therefore, the other squares in the line (marked in magenta) cannot be 7, 8, or 9. This is in fact the same situation as that in example 1.
Naked triples are notable more difficult to find than naked pairs. However, you will need to use naked and hidden triples to solve higher-level problems.