A punch-code lock box - Math Central

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Question from Doug:

I am a real estate agent that uses punch-code lock boxes on houses to store the keys. I need to crack the code on one of our boxes, so I need a list of the possible combinations.
Rules:
4 digit code
Numbers 0-9
Each number can only be used once
Order of the numbers does not matter.

With advice from this site, I have calculated that there should be 210 possibilities.
10x9x8x7 (5040) gives me the total number possibilities and 4x3x2x1 (24) gives me the total number of ways to arrange those numbers.
So if I divide the possibilities by the arrangement, I get 210. (5040 / 24 = 210) GREAT!!!

Now, how do I develop a list of those 210 combinations?

Thanks for your help.

Doug,

Work systematically, increasing each digit to the top before changing the one before it and restarting at the next one not

0-1-2-3, 0-1-2-4,...,0-1-3-4, 0-1-3-5,....,
0-1-8-9,0-2-3-4,0-2-3-5,...,0-7-8-9,1-2-3-4,...,6-7-8-9.

This may seem daunting but the cycles get shorter as you work upwards.

Good Hunting!
RD

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