A 5 digit push combination lock

HOME

Math Central

Quandaries & Queries

Question from Andrew:

I have a 5 digit push combo lock that i forgot the combo for. it has numbers 1-4 and each number can be pressed more then once ie. 11111, 36356
is there an algorithm out there that will list out the possible combinations for me? or maybe a way i could write them out myself.

thank you for your time.

Andrew,

You have a 5 digit push combination lock and each digit can by 1, 2, 3 or 4. Think of this as an old style odometer in a car, not the digital type but the numbers that rotate. The smallest number possible is

11111

followed by

11112

then

11113
11114.

Then the last 2 dgits roll over to give

11121
11122
11123
11124
11131
11132

and so on.

I hope this helps,
Penny

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.