### Lastly - Well

What are the last two digits of 2^(2^2003)?

### Lesser Digits

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

### Mini-max

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?

# Six Times Five

##### Age 11 to 14 Challenge Level:

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