Try to defeat the hydra!

The hydra currently has: segments, heads, and depth . Hercules has cut heads so far.

Click on a head to chop it off.

Nodes which have just grown back are shown slightly blueish ().

Mathematical fact: no matter what you do and no matter how much the hydra chooses to replicate when you cut off its heads, the hydra will always be defeated in a finite amount of time. (Of course, in this particular JavaScript implementation, the hydra is very tame, and only actually grows parts back when it won't clutter the display too much. So it's really very easy to defeat the hydra.) Metamathematical fact (needs to be checked precisely): the previous mathematical fact (suitably formalized) cannot be proven in Kripke–Platek set theory (essentially, because it requires a transfinite induction on the Bachmann–Howard ordinal, which is the proof ordinal of Kripke–Platek).

Restart with a new hydra.

Undo previous move (only one level of undo).

Start auto play or stop auto play.