Sudoku technique 7 of 12
Naked triple
Three cells in one unit holding only three digits between them own those digits.
What is a naked triple?
A naked triple is three cells in the same row, column or box whose candidates, taken together, are just three digits. Those three cells must use up all three digits between them, one each, so no other cell in the unit can hold any of them.
The cells do not each need all three candidates. Cells holding 1-5-8, 1-5-8 and 5-8 make a naked triple; so do 1-5, 5-8 and 1-8. What matters is that three cells share exactly three digits.
How to spot a naked triple
Look at the cells in a unit that have two or three candidates, and try them in groups of three: combine their candidates and see whether you get exactly three digits. Cells with two candidates are the best starting point, because two of them that share one digit, such as 1-5 and 5-8, only need a third cell drawn from the same three digits.
Triples hide better than pairs, because no two of the cells need to look alike. If a unit has many empty cells and several of them are short of candidates, it is worth checking for one before reaching for anything more exotic.
A worked example
Position from an Expert puzzle dealt by our Sudoku generator, pencilled in from the digits alone. Our game's own solver stops at naked pairs, so this step is beyond it; we checked that no simpler technique in this guide moves this position forward.
Cells are named by row and column: r4c1 is row 4, column 1. Rows count from the top, columns from the left, and boxes are numbered 1 to 9 reading like a book, so box 1 is top-left and box 9 is bottom-right.
This position comes from an Expert puzzle our game dealt, with every candidate pencilled in from the digits on the board. No single, pointing pair, box-line reduction, naked pair or hidden pair moves it forward. Look at row 5, which has eight empty cells. Three of them sit side by side: r5c3 holds 5 and 8, and r5c4 and r5c5 each hold 1, 5 and 8.
Between them, those three cells have only three digits to share out, and each needs one, so they take the row’s 1, 5 and 8. No other cell in row 5 can be any of those digits. Two cells lose candidates: r5c1 drops 5 and 8, leaving 2 and 9, and r5c2 drops 5, leaving 2, 3 and 4.
No cell is solved straight away, which is common with triples: they narrow the board for the next step rather than finishing it. Note too that r5c3 is in box 4 while the other two are in box 5, so this is a deduction about the row only.
Why it works
Row 5 needs one 1, one 5 and one 8. The cells r5c3, r5c4 and r5c5 cannot hold anything else, and no two of them can hold the same digit, so they take all three. If r5c1 were 5, for example, those three cells would have only 1 and 8 left to share, and one of them would be left with no digit at all.
Which difficulty levels need it
Expert only. Our game's own solver stops at naked pairs, and any puzzle it cannot finish with those is rated Expert, so no Easy, Medium or Hard puzzle needs a naked triple.
We measured 3,000 Expert puzzles our generator dealt. A solver that always tries the simplest technique first made a move with a naked triple in 332 of them. For 17 (0.6%), a naked triple was the hardest technique the puzzle needed: everything simpler stalls, and adding it finishes the grid. Of the 719 puzzles that the twelve techniques in this guide finish on their own, 5 cannot be finished without it. The rest of our Expert puzzles need techniques this guide does not cover yet, almost all of them chains.
Related: Naked pair , Hidden triple .
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