Problem:
Find the number of positive integers less than or equal to whose base-three representation contains no digit equal to .
Solution:
For , and there are -digit base-three numbers with digits of only and . Because , all the -digit base-three numbers less than that do not contain a begin with or . There are of them. Thus there are positive integers less than or equal to whose base-three representations contain no s.
The problems on this page are the property of the MAA's American Mathematics Competitions