Mondrian Puzzles

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An integer-sided rectangle can always be dissected into squares. Sometimes, a dissection exists where no two squares share a full edge, often called a nowhere-neat dissection.


When these rectangles are displayed with their squares ("solution as squares"), the smallest squares often cannot be seen well. A crushed version, topologically equivalent to the original dissection, uses rectangles instead of squares ("Mondrian solution"). These rectangle figures vaguely resemble the works of the artist Piet Mondrian (1872-1944).

These dissections can be used as puzzles. In the first type of puzzle, the row and column values corresponding to the crushed data are given ("Mondrian sums"). Logic can be used to determine the rectangles. In the second type, the empty grid of rectangles is given ("Mondrian algebra"). A solver can assign , , and values to various rectangles, and then values like to other rectangles. Eventually, algebra will completely solve the problem.


Contributed by: Ed Pegg Jr (July 2010)
Open content licensed under CC BY-NC-SA



Ed Pegg Jr, "Mathematical Games: Square Packings," Dec. 1, 2003.

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