  Let $I \subset K[x,y]$ be a monomial ideal. How small can $\mu(I^2)$ be in
terms of $\mu(I)$? It has been expected that the inequality $\mu(I^2) > \mu(I)$
should hold whenever $\mu(I) \ge 2$. Here we disprove this expectation and
provide a somewhat surprising answer to the above question.
