Naked Triple

When three cells see each other and have only three identical digits as candidates, the digits are called a Naked Triple. We can eliminate all the occurrences of these digits from cells that see all the Naked Triple cells. In classic Sudoku, all the cells of the Naked Triple are in the same region (same row, column, or box) and all the cells that see the Naked Triple cells must be in the same region.

Example 1

In the image below, in Row H, the digits 1, 2, & 4 in cells H2, H3, and H7 form a Naked Triple. These cells cannot contain any other digits. The rest of the occurrences of 1, 2, 4 in Row H (highlighted in red) can be eliminated.

Example 2

In Box 9 (highlighted with a red frame), the digits 1, 2, & 9 in cells G8, G9, and H7 form a Naked Triple. These digits must be in those cells. The rest of the cells in Box 9 cannot have the digits 1, 2, & 9, and these digits can be eliminated from them. In the example below, 1, 2, & 9 can be eliminated from I8 and I9.

Example 3

This is an interesting example. The rules for this board are both Classic Sudoku rules and Chess King rules, and the elimination works differently than in the previous examples. In Box 5, the only remaining unsolved cells form a Naked Triple. These cells must hold the digits 3, 7, & 9. Cell C5 sees each of the three cells of the Naked Triple, therefore 3, 7, & 9 can be eliminated from C5. C5 sees D5 and E5 because of Classic Sudoku rules, and it sees D4 (and D5) because of Chess King rules.