Paul Erdős in Jerusalem,
I just came back from a great Erdős Centennial conference in wonderful Budapest. I gave a lecture on old and new problems (mainly) in combinatorics and geometry (here are the slides), where I presented twenty problems, here they are:
Around Borsuk's Problem
Let $latex f(d)$ be the smallest integer so that every set of diameter one in $latex R^d$ can be covered by $latex f(d)$ sets of smaller diameter.