  We prove that colouring of pairs from aleph_2 with strong properties exists.
The easiest to state (and quite a well known problem) it solves: there are two
topological spaces with cellularity aleph_1 whose product has cellularity
aleph_2 ; equivalently we can speak on cellularity of Boolean algebras or on
Boolean algebras satisfying the aleph_2-c.c. whose product fails the
aleph_2-c.c. We also deal more with guessing of clubs.
