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Alternating sextet (Posted on 2007-03-30) Difficulty: 3 of 5
In the sequence 1, 0, 1, 0, 1, 0, 3, 5... each member after the sixth one equals the units' digit of the sum of the six preceding numbers of the sequence.

Prove that the subsequence 0, 1, 0, 1, 0, 1, will never occur.

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Some Thoughts Brute force and luck | Comment 4 of 6 |
(In reply to More brute force (spoiler) by Steve Herman)

It's obvious there must exist a cycle, and that it must be at most 1,000,000 "steps" long... it was good that this problem required only a 1456-step long cycle!
  Posted by Old Original Oskar! on 2007-03-31 09:07:38

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