TRY IT · GUIDED EXAMPLE
Find the hidden pair, strip the extras
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 where two colors are locked, strip their extra notes, then clear the box.
This is the real board from Marble Sudoku. The nine marble colors stand for the numbers 1 to 9.
- Pair
- Strip
- Clear
- Place
STEP 1
Find the hidden pair, strip the extras
Read the example in words
Row 3 has four empty holes. Their candidates are: column 3 Red or Sky, column 4 Red, Yellow or Navy, column 6 Red, Yellow or Navy, and column 7 Red or Sky. Yellow fits in only columns 4 and 6, and Navy fits in only those two as well: that is a hidden pair. The two colors are locked in those holes, so the extra Red notes are stripped from them. The holes now show exactly Yellow and Navy — a naked pair. They share the top-middle box, so Yellow is cleared from the box’s other holes: row 1 column 4, row 2 column 4 and row 2 column 6. Row 1 column 4 is left with Red alone, a naked single, and the Red marble is placed.
YOUR TURN · PRACTICE
Spot the hidden pairs
Every empty hole shows its candidates as small marbles. Tap the two holes where two colors are locked and watch the extra notes pop. On Easy the group glows. On Hard you search the whole board.
Why a hidden pair works
Say in one row the number 3 can only go in cells A and B, and the number 8 can also only go in A and B. One of them fills A and the other fills B — no third cell is left for either number. Both numbers are used up by those two cells, so any other candidate sitting in A or B can be deleted. The pair was hiding behind those extra candidates all along.
The same idea extends to three numbers: a hidden triple is three numbers that fit in only three cells of a group. Every other candidate can be removed from those three cells.
How to spot hidden pairs faster
- Scan one number at a time. Pick a number and check where it fits in a group. Two such passes usually surface the pair faster than rereading all the notes.
- Look in groups that are nearly full. Fewer empty holes means fewer possible spots, so numbers get locked sooner.
- Follow up with the naked pair. After stripping, the two cells show exactly the locked pair. Clear those two numbers from the rest of the group.
- Keep notes complete. A note you never wrote can hide a locked pair or fake one. Update notes every time you place a number.
Hidden pair vs. other pair techniques
| Naked pair | Hidden pair | Naked triple | |
|---|---|---|---|
| What you look for | Two cells with the same two candidates | Two numbers that fit only two cells in a group | Three cells whose notes use only three numbers |
| What it removes | Those two numbers from the rest of the group | All other candidates from those two cells | Those three numbers from the rest of the group |
| Level | Intermediate | Intermediate | Intermediate |
Common mistakes
- Any two shared candidates. Two cells that both show {3, 7, 9} prove nothing. Both numbers must be confined to exactly those two cells within the group.
- Stripping from the wrong cells. Only the two locked cells lose their extra candidates. The rest of the group keeps its notes.
- Forgetting the follow-up. After stripping, the two cells hold a naked pair. Clear those two numbers from the rest of the group.
- Confusing it with a naked pair. A naked pair looks at what two cells show; a hidden pair looks at where two numbers can go.
Hidden pairs FAQ
What is a hidden pair in Sudoku?
A hidden pair is two numbers that fit in only two cells of a row, column or 3 × 3 box, even if those cells show other candidates too. The two numbers are locked in those cells, so every other candidate can be removed from them.
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 hidden 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 hidden pair be in a box?
Yes. The two cells can share a row, a column or a 3 × 3 box. After stripping, the naked pair they become can be cleared from every group the two cells share.
What is a hidden triple?
A hidden triple is three numbers that fit in only three cells of a group. Every other candidate can be removed from those three cells.
Does this work in Marble Sudoku?
Yes. In Marble Sudoku the candidates are marble colors. Two colors that fit in only two holes of a row, column or box form a hidden pair.
PRACTICE IN THE GAME
Use hidden pairs in a real puzzle
Tougher puzzles are where pairs pay off. Note the possible colors, find two that fit in only two holes and strip the extras.
Next techniqueBox/line reduction
