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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?

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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?

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Six Times Five

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

Lastly - Well

Age 11 to 14 Challenge Level:
How can you simplify this so that it does not contain a power raised to a power?

Can you find a pattern in the last two digits? How about starting with some simple cases?