Comments by "disgruntledtoons" (@disgruntledtoons) on "The Hydra Game - Numberphile" video.

  1. There is a more radical form of this game where you take anu number, and express it as a sum of powers of two, and then express each exponent in that sum as a sum of powers of two, and so on, until no number greater than two is found in the entire express. Then for each step, subtract one from the expression, and increase each remaining two to three. Subtract one from this expression, and replace every remaining three with four. Continue with the process of subtracting one, and then replacing each remaining n with n+1. The number will soon grow beyond calculability, even with low starting values, but it is easily proven that the game will eventually end.
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