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A simple hydra game can be defined as follows: A hydra is a finite rooted tree, which is a connected graph with no cycles and a specific node designated as the root of the tree. In a rooted tree, each node has a single parent (with the exception of the root, which has no parent) and a set of children, as opposed to an unrooted tree where there ...
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Buchholz's paper in 1987 showed that the canonical correspondence between a hydra and an infinitary well-founded tree (or the corresponding term in the notation system associated to Buchholz's function, which does not necessarily belong to the ordinal notation system ), preserves fundamental sequences of choosing the rightmost leaves and the operation on an infinitary well-founded tree or the ...
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The King's Wise Men is one of the simplest induction puzzles and one of the clearest indicators to the method used. Suppose that there was one blue hat. The person with that hat would see two white hats, and since the king specified that there is at least one blue hat, that wise man would immediately know the colour of his hat.
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A sliding puzzle, sliding block puzzle, or sliding tile puzzle is a combination puzzle that challenges a player to slide (frequently flat) pieces along certain routes (usually on a board) to establish a certain end-configuration. The pieces to be moved may consist of simple shapes, or they may be imprinted with colours, patterns, sections of a ...