  Consider a large network with unknown number of nodes. Some of these nodes
coordinate to perform tasks. The number of such coordination groups is also
unknown. The only information about the network available is that any two
coordinating groups share at least $t$ nodes. To complete a particular task in
a day, at least $p$ nodes of the corresponding coordinating group must get
different time slots out of the $r$ available slots per day. Is there a way of
estimating the number of days required such that every coordinating group gets
at least one day where it can complete the task? As it turns out, this problem
is a special case of \textit{partially} perfect hash functions for intersecting
families.
