Chop a hydra's head off and it grows more back — can you ever finish it off?
A mathematical hydra is a tree of branching 'heads.' Cut one off, and the hydra sprouts several new copies of whatever was left below the cut, seemingly making your job harder no matter which head you choose. Is there any strategy that guarantees you eventually kill the whole hydra?
Reveal the answer
Yes: every strategy kills the hydra eventually, no matter how carelessly you chop, though it can take an almost incomprehensibly long time. Laurence Kirby and Jeff Paris proved this in 1982 using infinite ordinal numbers to show the hydra's 'size' always shrinks even while its head count explodes — and, remarkably, proved the fact can't be derived from ordinary arithmetic's own axioms alone.