**Problem**Let be natural numbers with . It follows from the pigeon-hole principle that there exist distinct subsets with . Is it possible to find such a pair in polynomial time?

This is one of a class of search problems for which a positive solution is garaunteed (so the corresponding decision problem is trivial) based on a theoretical property of the problem. Another such problem is given a Hamiltonian cycle in a cubic graph, find a second Hamiltonian cycle (here a theorem of Smith guarantee's a positive solution). The above problem is particularly attractive, since the proof that a pair must exist is quite simple, but it gives no insight into how to find the pair .

It seems to be consensus among the cryptography community that this problem is hard.