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.
Any ideas?


Hi Darrin,

There are many possible combinations to try.

  1. 10 one digit combinations
  2. 10 9 = 90 two digit combinations
  3. 10 9 8 = 720 three digit combinations
  4. 10 9 8 7 = 5040 four digit combinations
  5. 10 9 8 7 6 = 30240 five digit combinations
  6. ...
  7. ...
  8. ...
  9. ...
  10. 10! = 3628800 ten digit combinations.

I would start with the one digit combinations. It's easy to list them

0,1,2,3,4,5,6,7,8 and 9

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

01,02,03,04,05,06,07,08 and 09

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

012,013,014,015,016,017,018 and 019

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 am trying to map this out in Excel, and it occurs to me that this does not take into consideration that 143 equals 134, so there is one combination instead of two. Any 3 digits equal 1 combination. The same goes for 4 digits, 5 digits, etc. 12345 is the same as 54321 or 32415, etc.


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

0,1,2,3,4,5,6,7,8, and 9

The two letter words, in order are

01,02,...09; 12,13,...,19; 23,24,...,29; ...; 78,79; 89

The three letter words are

012,013,...,019; 023,024,...,029; ...; 089; 123,124,...129; 134,135,...,139; ...; 789

There are 120 possible three letter words.

Does this help?



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