Explorations of Finger Games

Daniel J. Tjie

Abstract


Finger Games, a topic in number theory, study certain 1-1 operations on sequences of 0’s and 1’s of length 2f - viewing the left and right half as fingers of adjacent hands interpreted using what is called Gray Code. In particular, Finger Games involve the operation of counting in Gray Code by an even number C, alternating hands. As the operations are  1-1, they divide the sequences into orbits. This paper focuses on the even parts of orbits for C = 6, 10, 14, and 18.



Keywords


Number Theory; Gray Code

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