Discovery / Constructive mathematics

The orthogonal mosaic

Complete the linked gaps in an intricate design, then find a route through its symbols.

0 creditsHuman example only

Your workbench

The paired-symbol mosaic

Fill 16 missing tiles in this 16 × 16 design. Each row and column must contain every large symbol 0–F once. Every pair of small background symbol and large tile symbol must occur exactly once across the board.

This public practice construction uses finite-field Latin squares. It preserves the pairing and transversal puzzle; it does not claim the production challenge’s non-group structure or cycle constraints.

Board interaction

Empty tiles16

Route rows selected12

Selected gap: row 1, column 1 · background 0

Experiment, make a prediction, and check your solution when ready.

Need a hint?

Rows with two gaps give a pair of candidate symbols. Cross-check their columns and background-symbol pairings. Finish the tile design before solving the four missing route rows.

Setting up your workbench…

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