Lesson 6 of 9
Hidden pairs
Two digits that can only go in the same two squares — so everything else in those squares goes.
What this grid does
- Starting digits
- 24 of 81
- Deductions to solve
- 60
- Uses of Hidden pairs
- 1
- Digits placed before it is needed
- 12
- First needed at
- deduction 15, in column 1 (R2C1 and R5C1)
- Also calls for
- last free cell, cross-hatching, naked single, hidden single and naked pairs
Measured on this grid by the same solver the hint button uses — how these puzzles are chosen.
Why this one is worth drilling
Only about 1 puzzle in 143 needs it. That is the whole reason this lesson exists: you cannot learn a deduction a random grid almost never asks you for, so it has to be set deliberately. That figure is measured rather than guessed: 0.7% of solvable 22-clue grids over 4,000 digs — about 1 in 140.
Hidden pairs are the hardest of these to see, and the measurement explains why: fewer than one random grid in a hundred needs one, so there is almost no chance to build the habit by playing. Most solvers meet it for the first time in a position they cannot move, with no idea this is what the position wants.
Where it sits in the nine
Sixth, directly after naked pairs, because the two are the same deduction read from opposite ends — one spots squares with only two candidates, the other spots digits with only two squares. Learning them apart is how solvers end up fluent in one and blind to the other, which is why they are adjacent here rather than separated by the box-line pair.
Working it
Count digits, not candidates. Take a unit and ask which two digits appear in exactly the same two squares, ignoring everything else those squares might hold. The clutter in the squares is what hides it — that is the whole reason for the name, and the reason reading squares rather than digits will not find it. A shortcut that makes them findable: in any unit, write down how many squares each missing digit can still occupy. Digits with a count of two are the only candidates for a hidden pair, and there are rarely more than three or four of them. Comparing those few against each other is a far smaller job than scanning squares, and it is why experienced solvers find hidden pairs quickly while beginners never see them.
The full explanation of hidden pairs covers the reasoning with diagrams.
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