Pair single

A cell whose only valid letter/digit pair is left is forced

How to use it

A naked single on the pair dimension. List the allowed pairs of a cell: its letter candidates times its digit candidates, minus every pair already placed somewhere in the grid and every pair a previous deduction has blocked at this cell. If exactly one pair survives, the cell takes it whole — letter and digit together.

It typically appears after orthogonality prunes have cornered a cell: a run of "this pair is used, that pair is ruled out" leaves exactly one combination standing. Placing the pair at once (rather than letter, then digit) keeps the trace readable and triggers both layers' peer eliminations together.

Why it is sound

The allowed pairs of a cell are exactly the letter/digit combinations a solution could assign there: both halves must respect their Latin rows and columns, and orthogonality forbids any pair already placed or blocked at the cell. With exactly one survivor, every solution assigns that pair.

A worked example

Count the allowed pairs of r1c2. The letter B never had a chance — the givens at r1c4 and r4c2 already cover its row and its column — so this is an A-cell. Among A's pairs at the cell, A1 is already placed at r3c1 and A3 at r4c4; the dead digits are struck by the earlier pair eliminations, leaving exactly one pair standing: A4. One pair standing means the cell resolves whole: place A4, and both layers' peers fall at once. This is the pair-dimension analogue of the naked single.