Quandaries and Queries
I have a puzzle question based on reality. I have a real-estate type keybox (Supra) that has 10 digits, 0-9. I am trying to figure out a methodical way to test all number combinations to it to open it. (totally legal- it was taken from the trash at a jobsite since they couldn't open it!) The combination could be any or all of the digits, but any digit is only used once. This is not like a simplex lock problem where a combination of keypresses would be different- i.e. 1,2,3 is the same as 1+2,3.
There are many possible combinations to try.
I would start with the one digit combinations. It's easy to list them
Each of these can be changed into nine, two digit combinations by appending a second digit. For example the one digit combination 0 can be changed into
List all 90 resulting two digit combinations. Each of these can be changed into eight, three digit combinations by appending a third digit. For example the two digit combination 01 can be changed into
List all 720 resulting three digit combinations. Each of these can be changed into seven, four digit combinations by appending a fourth digit.
This procedure gives an orderly way to list all the possible combinations. You can only hope that the unknown combination is only 3 or 4 digits long.
Darrin wrote back.
I didn't realize from your description that the order of the digits in a combination was not important. This reduces the number of possible combinations considerably. There are only 1023 possible combinations.
I am not an expert in Excel but from what I know I don't see a way to generate the possible combinations using Excel. You can list them all in an orderly way using lexicographic order, that is the order that would be used in a dictionary. Think of each possible combination as a "word" and order them as you would words in a dictionary.
The one letter words, in order are
The two letter words, in order are
The three letter words are
There are 120 possible three letter words.
Does this help?