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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