Consider all two digit numbers (10, 11, . . . ,99). In writing down all these numbers, which digits occur least often, and which occur most often ? What about three digit numbers, four digit numbers. . . .
How many six digit numbers are there which DO NOT contain a 5?
What is the last digit of the number 1 / 5^903 ?
How many positive integers less than or equal to 4000 can be written down without using the digits 7, 8 or 9?
What are the last two digits of 2^(2^2003)?
This article explains how credit card numbers are defined and the check digit serves to verify their accuracy.