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Problem of the Week 934

A Transformed Sequence

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An infinite sequence of digits "1" and "2" is determined uniquely by the following properties:

  1. The sequence is built up by stringing together pieces of the form "12" and "112".

  2. If we replace each "12" piece with a "1" and each "112" piece with a "2", then we get the original sequence back.

What is the 1000th digit in the sequence?

Source: St. Olaf College Problem of the Week for February 27, 2001

© Copyright 2001 Stan Wagon. Reproduced with permission.

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6 Apr 2001