Combination lock - Math Central

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Question from Antony:

Hello.
So my 3yr old daughter has had a bit of a play with the 3 dial combination lock on my backpack and locked it closed.
I am looking for all the possible combinations to go through a process of elimination to find the combination she has set.
To be clear. There are three dials, each with the numbers 0-9. I have read 10x10x10=1000 options but not sure if that is correct .. feels too small ?
Many thanks in advance.

Hi Antony,

1000 is correct, you have 10 choices for each of the three dials so that's $10\times10\times10$ choices.

If you are going through them to identify her combination I would do so in "numerical order" starting at zero.

000
001
002
.
.
009
010
011
.
.
020
.
.
999

This gives another verification that there are 1000 possible combinations, the numbers from zero to 999.

Penny

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