  Given $n$ pairwise disjoint sets $X_1,\ldots, X_n$, we call the elements of
$S=X_1\times\ldots\times X_n$ strings. A nonempty set of strings $W\subseteq S$
is said to be well-connected if for every $v\in W$ and for every $i\, (1\le
i\le n)$, there is another element $v'\in W$ which differs from $v$ only in its
$i$th coordinate. We prove a conjecture of Yaokun Wu and Yanzhen Xiong by
showing that every set of more than $\prod_{i=1}^n|X_i|-\prod_{i=1}^n(|X_i|-1)$
strings has a well-connected subset. This bound is tight.
