Math CentralQuandaries & Queries


Question from Jacqui:

Hi I need to break a code on my pedometer. I have only 3 digits 1 2 and 3 but need to fill a 5 digit code. I have tried to find answers but they seem to relate to if the digits are only used once. I can
use them in any order and repeated as many times. How many possibilities are there and is there an easy way to run through them.
Many thanks

Hello Jacqui,

Since your code is 5 digits in length we imagine these as 5 slots. Since you have 3 numbers to choose from to fill each of the slots and repetition doesn't matter, the number of possible codes is 3*3*3*3*3 = 243.
This is a relatively small number of possibilities (especially when it comes to codes), so checking them by hand is not a 'terrible' job. (If you can check one possibility per second, then you can finish in about 4 minutes) Start with 11111, and move up by one each time it does not work.

11131, and so on...

Good luck,

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