In mathematics, specifically in graph theory and number theory, a hydra game is a single-player iterative mathematical game played on a mathematical tree called a hydra where, usually, the goal is to cut off the hydra's "heads" while the hydra simultaneously expands itself.

2008年2月2日 · About the game A hydra is a finite tree, with a root at the bottom. The object of the game is to cut down the hydra to its root. At each step, you can cut off one of the heads, after which the hydra grows new heads according to the following rules:

2014年6月4日 · Imagine that you are Hercules, and you were given the task to slay the Hydra. Here is one possible hydra: I Just Got Trump’s “Buyout” Offer at My Job. Let Me Tell You How That’s Going. Our hydra...

2019年9月29日 · We assign an ordinal number to each hydra, in such a way that cutting off a head produces a hydra with a strictly smaller ordinal. As we play the hydra game, the sequence of hydras we encounter produces a corresponding sequence of ordinals.

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.

2024年4月18日 · You start with the Hydra being a straight line of vertices and edges, with a single root and a single leaf. At each step, call it k k, you always pick the right-most leaf/head and chop it off, whereafter k k leaves will regrow from the grandfather …

The Kirby-Paris hydra game is a one-player game played on a tree that can last a very large number of turns. [1] It gives rise to a function Hydra (n) that eventually dominates all recursive functions which are provably total in Peano arithmetic, and is itself provably total in PA + " ε 0 is well-ordered", and the game is also related to ...

2024年4月19日 · Tom talks Hercules and the Hydra Game. A single branch length 5, each time you chop off the right-most head, n grow back from the grand-parent (where n is the step number you are currently at). Q: How many steps to kill the Hydra? A: We have no idea…

In mathematics, especially mathematical logic, graph theory and number theory, the Buchholz hydra game is a type of hydra game, which is a single-player game based on the idea of chopping pieces off a mathematical tree.

2020年6月7日 · Hydras are a classic iterative game played on trees, known by googologists for the fast-growing functions derived from them and by serious mathematicians for their contributions to ordinal analysis.