What is a naked pair?
A naked pair is two cells in the same row, column or 3 × 3 box that have exactly the same two candidates. One cell gets the first number and the other gets the second. You may not know which is which yet, but both numbers are used up, so you can remove them from every other cell in that group.
A naked pair does not place a number by itself. It removes candidates, and that usually reveals a naked single or hidden single. In Marble Sudoku the candidates are marble colors shown as small marbles.
Use one in 3 moves
- 1Notes. Write the candidates for the empty cells in a group.
- 2Pair. Find two cells whose notes are the same two numbers.
- 3Clear. Remove those two numbers from every other cell in the group.
Then look for singles in the cells you changed.
TRY IT · GUIDED EXAMPLE
Find the pair, clear the row
Every hole in the glowing row shows its candidates as small marbles. The large copy of the row under the board shows the same holes up close. Find the two holes with the same two colors, then clear those colors from the rest of the row.
This is the real board from Marble Sudoku. The nine marble colors stand for the numbers 1 to 9.
- Pair
- Clear
- Place
STEP 1
Find the pair, clear the row
Read the example in words
Row 5 has four empty holes. Their candidates are: column 1 Yellow or Purple, column 6 Yellow or Purple, column 8 Red, Teal, Yellow or Purple, and column 9 Teal, Yellow or Purple. Columns 1 and 6 form a naked pair: they must take Yellow and Purple between them. Removing Yellow and Purple from the other two holes leaves column 9 with only Teal, a naked single. Once Teal is placed, column 8 is left with only Red.
YOUR TURN · PRACTICE
Spot the naked pairs
Every empty hole shows its candidates as small marbles. Tap the two holes that form a naked pair and watch their colors vanish from the rest of the group. On Easy the group glows. On Hard you search the whole board.
Why a naked pair works
Say two cells in a row can each only be 3 or 7. If one of them is 3, the other must be 7, and the other way around. Either way, the row’s 3 and the row’s 7 both sit in those two cells. No other cell in the row can hold a 3 or a 7, so you can delete them from all the other notes.
The same idea extends to three cells: a naked triple is three cells in one group whose notes together use only three numbers. Those three numbers can be removed from the rest of the group.
How to spot naked pairs faster
- Look for two-note cells first. Only cells with exactly two candidates can form a naked pair. Scan for them before anything else.
- Check all three groups. Two matching cells might share a row, a column or a box. If they share a row and a box, you can clear both.
- Keep notes clean. A missing or extra note hides pairs. Update notes every time you place a number.
- Follow up immediately. After clearing, look for new singles in the changed cells. That is where the payoff is.
Naked pair vs. other pair techniques
| Naked pair | Hidden pair | Pointing pair | |
|---|---|---|---|
| What you look for | Two cells with the same two candidates | Two numbers that fit only two cells in a group | One number whose box spots line up |
| What it removes | Those two numbers from the rest of the group | All other candidates from those two cells | That number from the rest of the line |
| Level | Intermediate | Intermediate | Intermediate |
Common mistakes
- A third candidate sneaks in. If one cell shows {3, 7, 9}, it is not a pair cell. Both cells must show exactly the same two numbers.
- No shared group. Two {3, 7} cells in different rows, columns and boxes prove nothing.
- Clearing outside the group. Only remove the pair numbers from cells in the group the two cells share.
- Guessing the order. The pair does not say which cell gets which number. Wait for another deduction to decide.
Naked pairs FAQ
What is a naked pair in Sudoku?
A naked pair is two cells in the same row, column or 3 × 3 box that have exactly the same two candidates. Those two numbers must go in those two cells, so they can be removed from every other cell in that group.
What is the difference between a naked pair and a hidden pair?
A naked pair is two cells that contain only the same two candidates. A hidden pair is two numbers that can only go in the same two cells of a group, even if those cells have other candidates too.
Does a naked pair tell me which number goes where?
No. It only proves that the two numbers fill the two cells. Another deduction later decides the order.
Can a naked pair be in a box?
Yes. The two cells can share a row, a column or a 3 × 3 box. If they share a row and a box, you can remove the pair numbers from both groups.
What is a naked triple?
A naked triple is three cells in one group whose candidates together use only three numbers. Those three numbers can be removed from the rest of the group.
Does this work in Marble Sudoku?
Yes. In Marble Sudoku the candidates are marble colors. Two holes that can each only take the same two colors form a naked pair.
PRACTICE IN THE GAME
Use naked pairs in a real puzzle
Tougher puzzles are where pairs pay off. Note the possible colors, spot two matching holes and clear the rest of the group.
Next techniquePointing pairs
