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Real-Life Math

You're a young but highly motivated crossword puzzle constructor whose puzzles have already appeared on the Internet and in many local publications. Now you've set your sights on the most prestigious piece of real estate in the crossword-puzzle universe: the pages of the New York Times.

But before you start to construct your grid, you wisely decide to do some homework. You research what the Times asks of constructors submitting crossword puzzles for its consideration.

It publishes grids in three different formats -- 15 x 15, 21 x 21 and 23 x 23 -- and strongly discourages the use of too many black squares.

"As a general rule," writes crossword puzzle constructor Coral Amende in her book, "no more than one-sixth of the grid should be black squares." She also suggests that beginners start out small -- say with a 15 x 15 grid.

If you follow Amende's advice and work on a 15 x 15 grid for your first crack at the Times, what is the maximum number of black squares that you can use?

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