  The purpose of this article is to demonstrate the connection between the
properties of the Gromov--Hausdorff distance and the Borsuk conjecture. The
Borsuk number of a given bounded metric space $X$ is the infimum of cardinal
numbers $n$ such that $X$ can be partitioned into $n$ smaller parts (in the
sense of diameter). An exact formula for the Gromov--Hausdorff distance between
bounded metric spaces is obtained under the assumption that the diameter and
cardinality of one space are less than the diameter and Borsuk number of
another, respectively. Using the results of Bacon's equivalence between the
Lusternik--Schnirelmann and Borsuk problems, several corollaries are obtained.
