A 12 digit number is formed using these rules:

* You can only use digits 1,5 and 9 (base 10)
* The number is divisible by 37

Prove that the sum of the digits is not 76

I'm sure what's wanted is a deductive proof, rather than a proof by testing all the qualifying numbers for their sum of digits. However, a tabulation of how many of each possible sum of digits might give someone a lead on a deductive proof:

sum of digits   number of occurrences
 12                     1
 24                    64
 36                  1000
 48                  4096
 52                   192
 56                   228
 60                  6859
 64                   228
 68                   192
 72                  4096
 84                  1000
 96                    64
108                     1

Posted by Charlie on 2007-01-22 11:26:10