LeafyOrb

Sudoku techniques · Hard level

Naked triples: three cells, three digits

A naked triple is three cells in the same row, column or box whose candidates, taken together, are only three digits. Those three cells must take those three digits, so you can remove them from every other cell in that row, column or box.

How it works

It is a naked pair with one more cell. Say three cells in a box allow 5 or 8, 6 or 8, and 5, 6 or 8. Three cells need three different digits, and these can only choose from 5, 6 and 8, so they use all three between them. No other cell in the box can be 5, 6 or 8.

The trap is that each cell does not need all three digits. Two candidates each is enough, as long as the three cells use no more than three digits in total. That is why naked triples are easy to miss.

  • The row, column or box the move uses
  • The cells that make the pattern
  • Candidates the move removes
Naked triple example on a Sudoku board: R7C9, R8C9 and R9C9 share just three digits (5, 6 and 8), so in box 9 no other cell can use them.

Example 1 · Box · from Hard puzzle #179

In box 9, the candidates are R7C9 (6 or 8), R8C9 (5, 6 or 8) and R9C9 (5 or 8). Between them the three cells use only 5, 6 and 8, so those three digits go in these three cells. Remove 8 from R7C7, R8C8, R9C7 and R9C8.

Play this position in Ninebloom: Home › Your own puzzle, then paste the code. NG-1A4R26-EYY7G3-TW4NUS-G3IANP-IF1KF6-8OIFQZ-0821EL-A7TIG8-ASKCG

Cells are named by row and column: R4C3 is row 4, column 3. Boxes are numbered 1 to 9, left to right and top to bottom.

How to spot it

  1. Fill in pencil marks for the row, column or box you are checking.
  2. Look at the cells with two or three candidates.
  3. Find three of them whose candidates, put together, are only three digits.
  4. Remove those three digits from every other cell in the shared row, column or box.

More examples

Naked triple example on a Sudoku board: R1C5, R1C8 and R1C9 share just three digits (1, 4 and 5), so in row 1 no other cell can use them.

Example 2 · Row · from Hard puzzle #43

In row 1, the candidates are R1C5 (1, 4 or 5), R1C8 (1, 4 or 5) and R1C9 (1, 4 or 5). Between them the three cells use only 1, 4 and 5, so those three digits go in these three cells. Remove 4 from R1C3; 4 and 5 from R1C4; 1 from R1C6.

Play this position in Ninebloom: Home › Your own puzzle, then paste the code. NG-1HKM6F-PD2FFF-Q455X1-W2SWA1-L4AQOD-VSR1OA-PLW4ET-RCR4XL-S0V0S
Naked triple example on a Sudoku board: R1C9, R7C9 and R9C9 share just three digits (4, 6 and 9), so in column 9 no other cell can use them.

Example 3 · Column · from Hard puzzle #527

In column 9, the candidates are R1C9 (4 or 9), R7C9 (4 or 6) and R9C9 (6 or 9). Between them the three cells use only 4, 6 and 9, so those three digits go in these three cells. Remove 6 and 9 from R2C9 and R8C9.

Play this position in Ninebloom: Home › Your own puzzle, then paste the code. NG-16L3M4-RI9C58-C9TOXA-72Q208-RY4LNU-ZU5XGT-7F1A2A-I9VTI8-FXSQA

Common mistakes

  • Expecting every cell to show all three digits. 58, 68 and 568 is a triple, and so is 58, 68 and 56.
  • Letting a fourth digit in. If the three cells use four digits between them, it is not a triple.
  • Removing digits outside the unit. Clear only the row, column or box that holds all three cells.

Questions

Does each cell in a naked triple need all three digits?

No. Each cell needs two or three of them, and the three cells together must use exactly three digits.

Is there a naked quad?

Yes. Four cells that share four digits work the same way, but they are rare, and they are not one of the twelve techniques Ninebloom's hints use.

Which Ninebloom level uses naked triples?

Hard, together with box/line reduction.