  A subset $A$ of a Banach space is called Banach-Saks when every sequence in
$A$ has a Ces{\`a}ro convergent subsequence. Our interest here focusses on the
following problem: is the convex hull of a Banach-Saks set again Banach-Saks?
By means of a combinatorial argument, we show that in general the answer is
negative. However, sufficient conditions are given in order to obtain a
positive result.
