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12 digit number (Posted on 2007-01-22) Difficulty: 3 of 5
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

No Solution Yet Submitted by atheron    
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Hints/Tips unsatisfying proof, by exhaustion, but may serve as a hint | Comment 1 of 2
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
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