In a mathematics book "Which way did the bicycle go" were given a problem:
What is the smallest square into which you are able to fit 11 unit squares without overlapping.
There were no solution but was said that some research have been done. I am interested to see how one proves that there really is the smallest square for this problem? Is there some optimization books to learn such methods or does one use some kind of topological reasoning based on, say, compactness?