Flip the question. Instead of asking “what can this cell be?”, ask “where can this digit go inside one house?”
If digit 2 can only sit in one empty cell of a row, column, or box, then it must go there — even if that cell still shows other pencil marks. The digit was *hiding* among the noise.
Why it works
Each house needs every digit 1–9 exactly once. So digit D is owed to that house somewhere.
If D is blocked from every empty cell except one (by other Ds in crossing lines, or by filled cells), that last cell is the only place left that can pay the debt. Other candidates in that cell do not matter — D has nowhere else to go.
This is also called crosshatching: you cross out cells that see an existing D until only one hole remains. Most easy puzzles are mostly Hidden Singles.
How to spot it
Check boxes first, then rows and columns. A box∩line intersection is three cells; line∩line is one — boxes rule out space faster.
Demonstration
Remember the two rules: every house needs the numbers 1–9, and the same digit cannot appear twice in a house.
Look at the shaded house and pick a digit — here 2. That digit must live somewhere in this house.
Which empty cells are still allowed to hold 2? Any cell that already sees 2 in its row or column is blocked. The possible space shrinks further…
…and further as you cross out more blocked cells… until exactly one cell remains. That is a Hidden Single (crosshatching).
Place 2 there. Even if the cell had other candidates written, 2 had no other home in the house — so it must be this cell.
Example 1
Pick a house and a digit. Ask: where can that digit still go? Prefer boxes first.
In this house, 3 fits in only one empty cell.
Place 3 there. The house still owed that digit, and only one seat was left.
Example 2
Pick a house and a digit. Ask: where can that digit still go? Prefer boxes first.
In this house, 6 fits in only one empty cell.
Place 6 there. The house still owed that digit, and only one seat was left.