Number Bracelets

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Grade Vs Difficulty:
  EasyModerateChallengingPerplexing
1-2
3-4
5-6
7-8
9-10
11-12
13-14

Choose two numbers in f0; 1; : : : ; 9g to begin a sequence of dig-
its. The next digit in the sequence is the units digit of the sum of the two
preceding it in the chain. For example if one starts with 4 and 7, the sequence
starts 4; 7; 1; 8; 9; 7; : : : . A \number bracelet" is formed when the sequence re-
peats; one can think of it closing up on itself to form a loop. Explore!

http://www.geom.uiuc.edu/~addingto/number_bracelets/
number_bracelets.html