  In a mathematics workshop with $mn$ mathematicians from $n$ different areas,
each area consisting of $m$ mathematicians, we want to create a collaboration
network. For this purpose, we would like to schedule daily meetings between
groups of size three, so that (i) two people of the same area meet one person
of another area, (ii) each person has exactly $r$ meeting(s) each day, and
(iii) each pair of people of the same area have exactly $\lambda$ meeting(s)
with each person of another area by the end of the workshop. Using hypergraph
amalgamation-detachment, we prove a more general theorem. In particular we show
that above meetings can be scheduled if: $3 \ | \ rm$, $2 \ | \ rnm$ and $r \ |
\ 3\lambda(n-1)\binom{m}{2}$. This result can be viewed as an analogue of
Baranyai's theorem on factorizations of complete multipartite hypergraphs.
