Math CentralQuandaries & Queries


Question from Carol:

I have a lock that has 3 tumblers. The numbers are 0 - 9. I cannot recall what I set the combination to. How many combinations will there be with three numbers?

Hi Carol,

Are you old enough to remember when the odometer in a car was not digital but was a row of tumblers that scrolled through the digits

Image from

The image above has 6 tumblers and you only have 3. Your tumblers start at 000 and progress in numerical order through

000, 001, 002, 003, ... 009, 010, 012, ... 999

and at this point the odometer has shown you 1,000 strings of digits. As numbers they are the numbers from 0 to 999.

I hope this helps,

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