Sudoku technique 6 of 12
Hidden pair
Two digits confined to the same two cells of a unit clear every other candidate from those cells.
What is a hidden pair?
A hidden pair is two digits that, within one row, column or box, can only go in the same two cells. Neither digit has anywhere else to go in that unit, so the two cells must hold those two digits, one each. That leaves no room for anything else in them, and every other candidate in the two cells can be removed.
It is the mirror image of a naked pair. A naked pair is two cells with only two candidates; a hidden pair is two digits with only two cells. The cells of a hidden pair usually carry extra candidates that bury it, which is where the name comes from.
How to spot a hidden pair
Work digit by digit, as you would for a hidden single. Pick a unit and, for each digit it is still missing, count the cells where it could go. You are looking for two digits that each have exactly two spots, and the same two spots. A digit with three possible cells cannot be part of a hidden pair.
Nearly full units are the best place to look, and so are boxes where copies of two digits in the neighbouring rows and columns block them out of most cells. Once you find the pair, clear every other candidate from both cells.
A worked example
Position from an Expert puzzle dealt by our Sudoku generator, pencilled in from the digits alone. Our game's own solver stops at naked pairs, so this step is beyond it; we checked that no simpler technique in this guide moves this position forward.
Cells are named by row and column: r4c1 is row 4, column 1. Rows count from the top, columns from the left, and boxes are numbered 1 to 9 reading like a book, so box 1 is top-left and box 9 is bottom-right.
This position is from an Expert puzzle our game dealt. Every candidate is pencilled in from the digits on the board, and nothing simpler works: no single of either kind, no pointing pair or box-line reduction, and no naked pair that removes anything. Look at column 4. It has six empty cells, and the digits 3 and 8 can only go in two of them: r1c4 and r4c4. Every other empty cell in the column already has a 3 and an 8 in its row or its box.
So r1c4 and r4c4 must be the 3 and the 8 of column 4, in some order. r1c4 has nothing else, but r4c4 also lists 9, and that 9 has to go: the cell is already spoken for. With it gone, the only cell in column 4 that can still take a 9 is r2c4, so r2c4 is 9.
Nothing about r4c4 on its own gives the pair away: it shows 3, 8 and 9, and as far as its row and box are concerned a 9 is still possible there. Only counting where the 3 and the 8 can go in the column reveals it.
Why it works
Column 4 needs a 3 and an 8, and both can only go in r1c4 or r4c4. If r4c4 were 9, the 3 and the 8 would both need r1c4, which can hold only one digit. So r4c4 is not 9, and the same reasoning clears any extra candidate from the cells of a hidden pair.
Which difficulty levels need it
Expert only. Our game's own solver stops at naked pairs, and any puzzle it cannot finish with those is rated Expert, so no Easy, Medium or Hard puzzle needs a hidden pair.
We measured 3,000 Expert puzzles our generator dealt. A solver that always tries the simplest technique first made a move with a hidden pair in 1,175 of them. For 172 (5.7%), a hidden pair was the hardest technique the puzzle needed: everything simpler stalls, and adding it finishes the grid. Of the 719 puzzles that the twelve techniques in this guide finish on their own, 25 cannot be finished without it. The rest of our Expert puzzles need techniques this guide does not cover yet, almost all of them chains.
Related: Naked pair , Hidden triple .
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