Problem of the Week 1181
A Singular Function
Let a(n) be the total number of digits that are 1 that occur in 1, 2, 3, ..., n. Example: a(100) = 21. True or False: a(n) < n for all n >= 2.
Source: Suggested by Ed Barbeau, who cites an article by Peter Vanden Bosch: A singular function: A problem-solving parable, The Mathematics Teacher, 90 (1997), 390-393.
© Copyright 2014 Stan Wagon. Reproduced with permission.