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Problem of the Week 1180

A Champernowne Puzzle

Which of these is larger?

the total number of digits in the sequence 1, 2, 3, ..., 101180

or

the number of zero digits in the sequence 1, 2, 3, ... , 101181

Note: Champernowne's number is the real number 0.12345678910111213.... David Champernowne, while an undergraduate at Cambridge in 1933, proved that this is a "normal number": The digit distribution is, asymptotically, uniform.

Source: Not sure of original source. It was in the Konhauser files and is in Which Way Did the Bicycle Go, by Konhauser, Velleman, and Wagon.

© Copyright 2014 Stan Wagon. Reproduced with permission.

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27 May 2014