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A crossword puzzle's (usually square) grid has white squares and black squares. I define a crossword grid's "density" to be the ratio of the number of white squares to the total number of squares. Clearly, the larger the density the harder the crossword will be to construct, with a ratio of one being a grid with no black squares at all.

For example, a recent New York Times crossword is a 15-by-15 square with 42 black squares and 225-42=183 white squares for a "density" of 183/225, approximately 0.81.

Is there a term of art for what I am calling crossword puzzle density? If so, can someone provide a source for that term?

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    $\begingroup$ In linear algebra, the term density refers instead to the ratio of the number of nonzero elements to the total number of elements (not to the number of zero elements). $\endgroup$
    – RobPratt
    Commented May 8, 2023 at 2:16
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    $\begingroup$ You don't distinguish between checked white squares (where an Across and a Down cross) and unchecked ones. Is this what you intend? Checked ones make constraints that unchecked ones do not, and thus make it harder to fill the grid.. $\endgroup$
    – Rosie F
    Commented May 8, 2023 at 5:18
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    $\begingroup$ @RosieF most american crosswords (including nyt crosswords) have no unchecked white squares $\endgroup$
    – juicifer
    Commented May 8, 2023 at 17:00
  • $\begingroup$ @RobPratt is correct and I have changed the question to reflect his suggestion. $\endgroup$
    – rlandster
    Commented May 8, 2023 at 17:48

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I don't know a general term for the "density", but in the UK at least, "barred crosswords" have no black squares at all, merely thicker lines (bars) between some of the solution squares indicating the ends of words. You can read about them for example here: https://www.theguardian.com/crosswords/crossword-blog/2021/apr/12/crossword-blog-barred-weekend-puzzles

I also found https://www.cruciverb.com/index.php?action=ezportal;sa=page;p=21 which has as one of its rules for crossword setters:

  1. Do not use too many black squares. In the old days of puzzles, black squares were not allowed to occupy more than 16% of a grid. Nowadays there is no strict limit, in order to allow maximum flexibility for the placement of theme entries. Still, "cheater" black squares (ones that do not affect the number of words in the puzzle, but are added to make constructing easier) should be kept to a minimum, and large clumps of black squares anywhere in a grid are strongly discouraged.
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