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Latin square

As explained in Optimization Algorithms: AI techniques for design, planning, and control problems

A Latin square is an n × n array containing n symbols such that every symbol occurs exactly once in each row and column.

A Latin square is an n × n array of n symbols in which every symbol appears exactly once in every row and column. section 5.4

Sudoku adapts this structure into a constraint-satisfaction problem: its 9 × 9 grid must contain digits 1 through 9 exactly once in each row and column, with an additional requirement for each 3 × 3 region. section 5.4

Sudoku as an extended Latin square

A completed Sudoku grid satisfies the Latin-square conditions across rows and columns. Its nine 3 × 3 boxes impose extra constraints, making Sudoku more restrictive than an ordinary Latin square. section 5.4

How Optimization Algorithms: AI techniques for design, planning, and control problems covers it

How deep it goes
Defines the row and column uniqueness rule and connects it to Sudoku, but does not develop Latin-square construction or theory.
Examples
Uses a 9 × 9 Sudoku grid containing digits 1 through 9 in rows, columns, and nine 3 × 3 boxes.
What you can do after
Evaluate Sudoku as a Latin-square extension with additional subgrid constraints.
How it connects
Connects Latin squares with Sudoku, constraint satisfaction, and 3 × 3 subgrids.
Cover of Optimization Algorithms: AI techniques for design, planning, and control problems
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