Each of the ID numbers issued to Mr.Cooper and Mr. Duncan is of the form ABCDEFGHIJ, with each of the letters representing a different digit from 0 to 9 inclusively, such that:

(i) BCD is divisible by 2.

(ii) CDE is divisible by 3.

(iii) DEF is divisible by 5.

(iv) EFG is divisible by 7.

(v) FGH is divisible by 11.

(vi) GHI is divisible by 13.

(vii) HIJ is divisible by 17.

Determine the ID numbers issued to each of the gentlemen, given that the ID number of Mr. Cooper is greater than that of Mr. Duncan.

Note: A is not 0, and C is greater than D.

*** While a solution may be trivial with the aid of a computer program, show how to derive it without one.

(In reply to re(2): Hmmmmm.... (spoilers) by Dej Mar)

I don't think that "C greater than D" is otherwise implied, as that note rules out

4106357289
1406357289

unless you mean that one of these two would be ruled out by A greater than B. But that would still leave two others.

Edited on August 20, 2008, 10:18 am

Posted by Charlie on 2008-08-20 10:16:46