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Lesser Digits

How many positive integers less than or equal to 4000 can be written down without using the digits 7, 8 or 9?

The Codabar Check

This article explains how credit card numbers are defined and the check digit serves to verify their accuracy.

Six Times Five

How many six digit numbers are there which DO NOT contain a 5?


Age 11 to 14 Challenge Level:

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 and so on?