
Killing the Hydra (2013) - yread
https://markhkim.com/blog/mathematics/killing-the-hydra/
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dzdt
I don't understand the game rules fully. What happens if a head is cut off
which is connected directly to the root? Rule (2) says

 _Go to the node right below the node connected to the severed head—labelled
in purple in the diagram—and reproduce n copies of all the nodes and the
segments above the selected node. Here, n is the number of times Hercules has
attacked the Hydra thus far._

But if we cut off a head connected to the root, there is no node below the
root. So then what?

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syphilis2
I don't even see a way to reach a point where Hercules could cut off a head
directly attached to the root node without having already created more necks
and heads than what he destroyed. I'm probably missing the larger point of
this, but I don't see how the hydra can ever be killed.

I imagine a simple example of 2 necks of length 2 connected to the root. If
Hercules cuts off one head then at least one new neck of length 2 will grow in
its place, always creating a scenario worse than before. What am I missing?

~~~
syphilis2
I looked around online and the description of the game in this article is
inaccurate. When a head is severed the only node that is duplicated is the
parent to the head (along with all its remaining children). I originally
believe that all children of the head's grandparent were to be copied.

 _Go to the node right below the node connected to the severed head—labelled
in purple in the diagram—and reproduce n copies of all the nodes and the
segments above the selected node._

Compared to [http://googology.wikia.com/wiki/Kirby-
Paris_hydra](http://googology.wikia.com/wiki/Kirby-Paris_hydra)

 _We start with a finite rooted tree T. Call its root R.

Jonathan picks a leaf vertex of the tree and a natural number N. Call the leaf
A and its parent B:

A is deleted from T.

If B = R, nothing happens. Otherwise, let C be the parent of B. Consider the
subtree consisting of B and all its children; copy this subtree N times.
Attach all these copies to C._

