Cyclic Latin Square Generator

Cyclic Latin Square Generator

This page generates a cyclic Latin square from one integer order n, default 4 and accepted range 1 to 100. Each of n symbols occurs exactly once in every row and column. It does not generate general block designs or randomized assignments.

The entry at zero-based row i and column j is ((i+j) mod n)+1. Every row shifts the previous row by one symbol. The output is deterministic, with tabs between columns and newlines between rows.

For n=3 the rows are 1 2 3, then 2 3 1, then 3 1 2. For n=1 the output is the single symbol 1. The maximum order 100 generates 10000 table entries.

There is no randomization, custom symbol list, orthogonality test, pairwise coverage guarantee or balanced incomplete block design mode.

The square is computed locally in the browser and can be copied as tab-separated text into a spreadsheet. These layouts illustrate cyclic Latin squares; applications to experimental assignment need separately justified randomization and study design.