multi-party Communication complexity of "Set Partition problem"
A linear lower bound on deterministic CC follows by fixing one of the sets to be empty.

For a randomized logarithmic upper bound, first note that this problem can be reduced to the problem asking whether the sum of three $3n$-bit numbers is exactly $2^{3n}-1$.  This one can be solved in $O(\log n)$ randomized communication by the players operating mod a random $O(\log n)$-bit prime.