Overview
A Latin square is a grid where every symbol appears once per row and once per column. This tiny 3×3 case shows how constraint propagation forces every remaining cell.
How to solve The 3×3 Latin Square
- Find a row or column missing only one value — that value has exactly one home.
- Fill it, which shrinks its row and column, exposing the next forced cell.
- Repeat until the grid is complete — no guessing is ever required.
The key insight
Solve the most constrained cell first. A cell with one candidate left removes options elsewhere, cascading to a unique solution.
Variations & echoes
- Sudoku is a 9×9 Latin square with extra box constraints, solved the same way.
- Latin squares underpin experimental design and error-correcting codes.
Frequently asked questions
How many 3×3 Latin squares exist?
There are 12 in total, but with three well-chosen givens the completion is unique.