conundrum

a difficult puzzle or problem with no easy answer

A conundrum is a knot of a problem: each obvious tug seems to tighten another strand.

The team faced a conundrum: lower the price and lose money, or keep the price and lose students.

Conundrum is not just any problem. It is the kind where each simple answer creates another problem.

Picture a knot on the desk. One strand looks easy. You pull it, and the knot tightens. That is a conundrum.