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Fibonacci Bracelets
You can make "bracelets" using Fibonacci-like sequences of numbers. Here's how:
Choose any pair of one-digit numbers. Make a Fibonacci-like sequence by recording only the units digit of the sum of these numbers and subsequent number pairs.
For example, the sequence starting (1,3) makes the following pattern:
1, 3, 4, 7, 1, 8, 9, 7, 6, 3, 9, 2, 1, 3, . . .
Eventually the sequence repeats (in the example above, after the number 2). At this point, attach the last digit in the sequence to the first digit, thus making a bracelet of digits.
<--- 1, 3, 4, 7, 1, 8, 9, 7, 6, 3, 9, 2, --->
Note that sequences starting with any clockwise consecutive pair of numbers in the circle will make the same bracelet. Thus (3,4), (7,1), (1,8), etc. will result in the same bracelet. You should note, however, that although the pair (1,3) is in this bracelet, the pair (3,1) is not.
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