The following two problems are addressed in this paper. Let $k \geq 2$, $\k$ be a $k$-element set and $M$ be a family of maximal partial clones with trivial intersection over $k$. What is the smallest possible cardinality of $M$? Dually, if $F$ is a family of minimal partial clones whose join is the set of all partial functions on $k$, then what is the smallest possible cardinality of $F$? We show that the answer to these two problems is three.
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