Pointing pairs vs naked pairs in Sudoku

A pointing pair confines one digit to two cells in a box that share a row or column. It removes that digit from the same line outside the box. A naked pair confines two cells in one unit to the same two digits. It removes those digits from the other cells in that unit.

“Pair” refers to two different things here: two possible homes for one digit, or two digits reserved by two cells. Neither pattern tells you which member of the pair goes where.

Pointing pair: one digit points out of a box

Check the top-left box for 6. Row 3 already has 6 at c6, excluding its blank cells in the box. Column 2 has 6 at r7c2, excluding its blanks. Column 3 has 6 at r7c3, excluding its blanks. The only places left in box 1 are r1c1 and r2c1.

Both are in column 1. Whichever takes the 6, box 1 supplies column 1’s 6. Therefore any other candidate 6 in column 1, outside box 1, can be erased.

Every elimination in this example: remove 6 from r6c1, changing its candidates from 3,6,8,9 to 3,8,9. No other empty cell outside box 1 in column 1 currently has candidate 6. There is no permission to remove 6 from unrelated columns or from either member of the pair.

The two marked cells have other candidates. That is fine: the condition is about all the possible locations for 6 within the box, not their full lists.

Naked pair: two cells reserve two digits

Here r1c4 and r1c5 both have the complete candidate list 4,6. They share row 1 and the top-middle box. One must take 4 and the other 6. Row 1 cannot use either digit anywhere else.

The pair also shares box 2, so it reserves 4 and 6 there. Every permitted elimination is listed below; no other cell in either shared unit contains those candidates.

The cleanup makes r1c2 a single 5 and r2c6 a single 9. The other three cells remain undecided.

Do not remove 4 or 6 from the rest of column 4 or column 5. The pair does not reserve both digits in either of those columns, because the two cells are in different columns.

A near-match that is not enough

Now change one fact: remove the given 9 at r1c1 from the second grid. This modified puzzle still has one solution, but its immediate candidate lists change.

r1c4 still has 4,6; r1c5 now has 4,6,9. The latter might be 9, so those cells do not reserve 4 and 6. You cannot use this supposed pair to erase 4 from r1c2. The final answer may still be 5, but this particular argument no longer proves it.

Similarly, a pointing pair fails if another cell elsewhere in the box can accept the digit. Two conveniently aligned candidates are not enough; they must be the only locations for it in the box.

Before you erase a candidate

1. Check that the relevant notes are complete and current.
2. Name the pattern: one digit locked to a line, or two cells holding two digits.
3. Name the shared unit and the exact cells affected.
4. Erase only the candidates the argument excludes, then look for singles.

HoDoKu explains naked subsets in more detail. Our pencil-mark guide covers note cleanup, and the Sudoku overview puts these techniques in a solving sequence. Use More puzzles in Puzzle Lantern Sudoku when you want another grid; a particular technique is not guaranteed on every puzzle.