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Costas Array Sudoku

The numbers 1--9 must each appear exactly once in each row, column, block, and color. Note that each colored region is disconnected; for example, the red region is the set of all nine of the red cells.


Appeared in The Big Notebook, a publication of the Mathematical Association of America's Special Interest Group on Mathematics in Business, Industry, and Government, Volume 2, Number 2, August 2006. The puzzle's title reflects the fact that the set of red cells forms a Costas array.