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: Hmmmmm.... (spoilers) by Jyqm)

Similarly by brute force, I, also, came to the same conclusion as you and Charlie. Yet, I found the number of possible solutions as six, not four:

Mr. Cooper 4160357289
Mr. Duncan 4130952867

Mr. Cooper 4160357289
Mr. Duncan 1460357289

Mr. Cooper 4160357289
Mr. Duncan 1430952867

Mr. Cooper 4130952867
Mr. Duncan 1460357289

Mr. Cooper 4130952867
Mr. Duncan 1430952867

Mr. Cooper 1460357289
Mr. Duncan 1430952867


Perhaps K Sengupta meant to indicate in the note that A is greater than B. If such is the case, then there is only one solution:

Mr. Cooper 4160357289
Mr. Duncan 4130952867
 

Edited on August 20, 2008, 4:30 pm

Posted by Dej Mar on 2008-08-19 22:37:13