Sudoku has a simple promise: every row, every column, and every 3×3 box must contain the numbers 1 through 9 — each exactly once.
When a house has only one empty seat left, you already know who sits there: the number that is still missing. That is an Open Single.
Why it works
A house is not allowed to skip a digit, and it is not allowed to repeat one. So if eight of the nine seats are taken, the ninth seat has no choice — there is only one digit left on the missing list.
You do not need pencil marks. Just count: which number from 1–9 is not in that house yet?
(Sometimes the same placement is also a Hidden Single — same answer, different story.)
Demonstration
Remember the rule: every row, column, and box must contain 1–9 exactly once.
Pick a house and ask: how many empty cells does it still have? Here one house is almost full — only one empty cell remains.
Make a tiny list of which digits are already in the house. Shrink the missing list further… until only one digit is left.
The missing digit is 3. Place it in the empty cell. That is an Open Single (also called *Last Digit*) — no guessing, just finishing the house.
Example 1
Find a house with only one empty cell.
List which digits 1–9 are already there. One digit is missing.
The missing digit is 1. Place it — the house still owed every digit 1–9, and only one seat was left.
Example 2
Find a house with only one empty cell.
List which digits 1–9 are already there. One digit is missing.
The missing digit is 9. Place it — the house still owed every digit 1–9, and only one seat was left.