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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 hea
by syphilis2 10y ago
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 10y agoI 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.