Naked Pair

Expert

Description

Find two cells in the same row, column or 3x3 block that each contain only the same two candidates. Those cells form a Naked Pair. Keep the two candidates in both cells, and remove those digits from every other cell in that group.

Why? The two cells cannot contain the same digit, and neither can contain anything outside the pair. One must hold the first digit and the other the second, in either order. Together they use both digits in their shared group, even before you know which goes where.

A Naked Pair removes candidates. It may reveal a Hidden Single or a Naked Single, or it may leave no cell ready to fill. In that case, keep working with the reduced notes: you may need several more eliminations, using this or other techniques, before you can place a digit. Those eliminations are progress too.

The examples below were chosen because a Hidden Single follows immediately, making the effect easy to see. We use pencil notes throughout: green candidates stay and red candidates are removed. Yellow highlights show all other occurrences of the digits being discussed; the shared group is shaded. The second picture shows that Hidden Single.

Example 1. A Naked Pair in a row

1. Naked Pair
In row 4, columns 4 and 9 each contain only 1 and 7, shown in green. Remove the red 1 from column 1. All other 1 and 7 candidates remain highlighted across the grid. In row 4, columns 4 and 9 each contain only 1 and 7, shown in green. Remove the red 1 from column 1. All other 1 and 7 candidates remain highlighted across the grid.
In row 4, the cells at columns 4 and 9 each allow only 1 and 7. Together they use both digits in the row, so remove the red 1 at column 1. There are no other 7s in the row to remove. One elimination is enough to help.
2. Hidden Single
After removing 1 from row 4, column 1, block 4 has only one 1 candidate: the green 1 at row 6, column 1. Other notes remain in that cell. After removing 1 from row 4, column 1, block 4 has only one 1 candidate: the green 1 at row 6, column 1. Other notes remain in that cell.
Now check all the 1s in block 4 (shaded). With row 4, column 1 ruled out, only the green 1 at row 6, column 1 remains. Place 1 there, even though the cell still has other candidates.

Example 2. A Naked Pair in a block

1. Naked Pair
In block 9, row 7, column 8 and row 9, column 9 each contain only 2 and 8. Keep these green notes. Remove red 2 from row 8, column 7, and red 2 and 8 from row 9, column 7. In block 9, row 7, column 8 and row 9, column 9 each contain only 2 and 8. Keep these green notes. Remove red 2 from row 8, column 7, and red 2 and 8 from row 9, column 7.
The two cells containing only 2 and 8 share block 9. They need not share a row or column. Keep their green notes, and remove 2 from row 8, column 7, plus 2 and 8 from row 9, column 7.
2. Hidden Single
After the Naked Pair removes 2 from row 8, column 7, the only 2 candidate left in row 8 is the green 2 at column 5. After the Naked Pair removes 2 from row 8, column 7, the only 2 candidate left in row 8 is the green 2 at column 5.
In row 8 (shaded), only one 2 candidate remains: the green 2 at column 5. Place 2 there. The pair's two cells still contain both 2 and 8; we have not decided their order.

The second example uses the same position as the first example in our Hidden Pair lesson. Here, the Naked Pair of 2 and 8 removes other copies of those digits from the block. There, the Hidden Pair of 1 and 6 removes other digits from its own two cells. Both describe the same restriction.

Demo

Click on arrow buttons or use arrow keys on your keyboard to navigate between slides. Tap on arrow buttons to navigate between slides.

How to find Naked Pairs

  1. Look for a cell with exactly two candidates, such as 7 and 8.
  2. Check its row, column and block for another cell containing only those same two candidates.
  3. Choose a group shared by both cells. Keep the candidates in the pair, and remove both digits from the other cells in that group wherever they occur.
  4. Recheck for Hidden Singles and Naked Singles. If no single is available, look for further candidate eliminations with this or other techniques.

Keep your notes complete and up to date. Highlighting both digits helps you follow the eliminations, but check the cells' entire candidate lists before declaring a pair. If one cell has just one candidate, place that Naked Single first.

Two matching notes are not enough

A cell with 5 and 6 and another with 5, 6 and 9 do not form a Naked Pair. The second cell could hold 9, so the two cells do not reserve both 5 and 6. The demo's final check shows this mistake on a real position.

Two cells containing only 5 and 6 must also share a row, column or block. Matching candidates in unrelated cells do not justify a Naked Pair elimination. The cells do not need to be adjacent.

Where to remove candidates

Remove the pair's digits only from other cells in a group shared by both pair cells. A cell that sees just one member of the pair is not restricted by the pair alone. Other digits in the affected cells stay, and both candidates in each pair cell stay.

If the two cells share both a block and a row or column, the same argument works in each shared group. Check each group separately. If there are no copies of either digit to remove in a group, the pair is valid there but makes no immediate progress. A pair that removes even one candidate can be useful.

Naked Pair or Hidden Pair?

A Naked Pair starts with two cells, each containing only the same two digits. Remove those digits from other cells in the shared group. A Hidden Pair starts with two digits whose only positions in a group are the same two cells. Remove other digits from those cells.

In a group with four empty cells, a Naked Pair leaves the other two missing digits for the other two cells: a complementary Hidden Pair. In the block example, the Naked Pair of 2 and 8 leaves only 1 and 6 in the remaining cells. Either view gives the same eliminations; use the one you notice first. These examples do not imply there is only one valid deduction.

Do not confuse either technique with a pointing pair. That name describes two positions for one digit in a block, aligned in one row or column. It does not require two matching candidate lists. See Pointing Candidates and Claiming Candidates for those intersection rules.

Try it yourself

These library positions were chosen so that each Naked Pair immediately reveals a Hidden Single. Singles and intersections have already been exhausted, and the links preserve the resulting pencil notes. Find the pair, remove its digits from the other cells in the group, then find that single.

Use Hint to check the pair. Applying that hint removes candidates; request the next hint to see the Hidden Single in these exercises. Naked Pair hints are available in Expert and Extreme games, with pencil notes. These practice links open directly in pencil mode.

See also

  • Review Sudoku Rules for why a group cannot repeat either digit.
  • Learn Naked Single to recognize a cell with just one candidate.
  • Learn Hidden Single to recognize the placements revealed here.
  • Compare Hidden Pair to understand the opposite direction of elimination.
  • Continue with Naked Triple to reserve three digits across three cells whose lists need not match.
  • Play Expert Sudoku online to combine pairs with singles, intersections and other techniques.