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ID Number And Digit Arrangement (Posted on 2008-08-19) Difficulty: 2 of 5
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.

See The Solution Submitted by K Sengupta    
Rating: 4.0000 (2 votes)

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Still puzzled | Comment 8 of 9 |

My recent post should have said "C was LESS THAN D, so excluded" ("greater" was typo).  I see that the four I have left are the same ones that Charlie listed (in reverse order) in the first post.  There are probably various ways which, given the initial specs (i.e. ten unique digits, and the seven divisibility conditions), we might impose other constraints to limit to a pair.  In any case, A must be either 1 or 4, so the "A is not zero" is redundant.  If the ID in question is drawn from the US Social Security Number, we would have a nine-digit identifier with a tenth added as a check digit in most systems.

I suppose we all used computer approaches, though invited to attempt without.  This may not be quite "trivial" but there could be competition for efficiencies (in execution cycles). Perhaps there are some WIKI lists of constraints imposed by the divisibility tests (e.g. D must be even if BCD divisible by 2). 

I guess we'll have to wait for KS to resolve our perplexity at this stage.

 


  Posted by ed bottemiller on 2008-08-20 11:56:55
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