Naked Triple (and Quad)

Level: first needed in Master puzzles. In one line: Three cells in a unit use only three numbers between them, so those numbers are removed from the rest of the unit.

A Naked Triple is three cells in the same unit whose candidates, taken together, are only three numbers. Each cell does not need all three: {4, 6}, {4, 7} and {4, 6, 7} is a naked triple on 4, 6 and 7. Those three cells will use up 4, 6 and 7 between them, so no other cell in the unit can hold any of them.

A Naked Quad is the same idea with four cells and four numbers. Quads are rare and hard to see, but the logic is identical.

Example from a real puzzle

This position comes from an Extreme puzzle in Sudoku Arena, at the exact moment the Naked Triple is the next logical move. Cells are named by row and column: R3C4 means row 3, column 4.

R1C2, R1C6, R1C7 hold only {4,6,7} in row 1. Result: remove 7 from R1C3, 6 from R1C5, 7 from R1C8.

Play this puzzle and look for the move yourself. It's a practice game, so it doesn't count towards your stats.

How to spot it

1. In a unit with several empty cells, look for cells with only two or three candidates.
2. Find three of them whose candidates together make just three different numbers.
3. Remove those three numbers from the other cells in the unit.

Tips

• Count the different numbers across the three cells, not the notes in each cell.
• When a unit has only four or five empty cells, a naked triple there is the same as a hidden pair in the remaining cells: look for whichever is easier.

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