Graeco-Latin square: n×n grid where each cell has a Greek and Latin letter pair. Each Greek letter appears once per row/col, each Latin letter appears once per row/col, and all n² pairs appear exactly once. Equivalent to a pair of orthogonal Latin squares.
How to Use
Enter n:
- Square: Greek-Latin pairs
- Verify: All pairs present
- Design: Blocking factors
Experimental Design
With a Graeco-Latin square, you can control THREE blocking factors simultaneously: rows, columns, and Greek letters. This extends the Latin square design. For a pharmaceutical trial: n treatments, n time periods, n patient groups, n clinics.
Existence
Exist for all n≥3 except n=2 and n=6. The n=6 impossibility (Euler's conjecture proved by Tarry, 1901) is famous. For prime n, simple modular arithmetic constructions work perfectly.
Step-by-Step Instructions
- 1Enter n.
- 2Generate square.
- 3View pairs.
- 4Verify uniqueness.
- 5Apply to design.