Packing 11 unit squares in a square

Letter from Martin Gardner, 1980-01-10

Best known packing, Walter Trump, 1979

This packing is absolutely rigid, no unit square can be rotated or translated.
Slight improvements of the packing are not possible.
Any improved packing has to have an essentially different geometrical arrangement of the unit squares.

For more details see:

Packing-11-squares.pdf

Dynamic construction of the packing

Improving packings

Reference:
Gardner, Martin. Fractal Music, Hypercards, and More Mathematical Recreations
from Scientific American Magazine. New York: W. H. Freeman, pp. 299-300, 1992.