Latin Square Solver
Simpler than Sudoku — fill each row and column with each symbol once. No box constraint. Choose a size from 4×4 to 9×9.
About Latin Squares
A Latin square of order n is an n×n grid filled with n different symbols so that each symbol appears exactly once in every row and every column. It is essentially Sudoku without the box constraint. The name comes from Leonhard Euler, who used Latin letters as symbols. Latin squares are the mathematical foundation of Sudoku, as every valid Sudoku is also a Latin square.
Latin squares have broad applications in experimental design, cryptography, and combinatorics. This solver supports orders 4 through 9. For each size the generator produces a random valid Latin square and removes cells based on difficulty, leaving you a logic puzzle to complete.
Frequently Asked Questions
What is the difference between a Latin square and Sudoku?
Sudoku is a Latin square with an extra constraint: the grid is divided into boxes, each of which must also contain each symbol once. A Latin square has only the row and column constraints.
Are Latin square puzzles easier than Sudoku?
Generally yes — without the box constraint, there are fewer deductions available, but the puzzles tend to require fewer given clues to be uniquely solvable.
How are the puzzles generated?
The generator fills the grid with a random valid Latin square using backtracking, then removes cells based on difficulty. Uniqueness of the solution is verified before presenting the puzzle.
What symbols does the Latin square solver use?
For sizes 4–9, the solver uses digits 1 through n. For a 4×4 Latin square, you fill the grid with 1, 2, 3, 4.
How to Play Latin Square
1 Rules
- ✓ Fill every row with each symbol exactly once — no repeats.
- ✓ Fill every column with each symbol exactly once — no repeats.
- ✓ Unlike Sudoku, there are no sub-box constraints — only rows and columns matter.
- ✓ Pre-filled clue cells cannot be changed.
2 Strategies
- 💡 Row Scan: Find rows with the fewest empty cells and complete them first — each placement creates new eliminations across the whole column.
- 💡 Column Cross-Check: For any empty cell, intersect the symbols missing from its row with those missing from its column — that intersection is your full candidate set.
- 💡 Naked Singles: If the cross-check leaves only one possible symbol for a cell, place it immediately and cascade the eliminations.
Tip: Latin Squares are the mathematical foundation of Sudoku — every valid Sudoku is also a Latin square. Mastering row-column elimination here will sharpen your instincts for harder Sudoku variants.