What is the smallest rectangle that can hold squares of sizes 1 to
? This problem is unsolved for more than 27 squares. The excess area in these packings is 0,1,1,5,5, 8,14,6,15,20, 7,17,17,20,25, 16,9,30,21,20, 33,27,28,28,22, 29,26. How the excess is bounded for higher
is an unsolved problem, but the bounds seem to be
and
.
