Suppose that the convex hull of the Minkowski sum of several compact connected sets in $\mathbb R^d$ contains the unit ball centered at the origin and the diameter of each set is less than $\delta$. If $\delta$ is very small (this smallness may depend on $d$ but on nothing else), does it follow that the sum itself contains the origin?



Minkowski sum of small connected sets
I finally figured it out. My solution is [here](http://www.artofproblemsolving.com/Forum/viewtopic.php?t=308020). I would repost it on mathoverflow but until LaTeX is enabled, it is quite hard for me to communicate such things here...


