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Velvet Ties (Posted on 2008-02-25) Difficulty: 2 of 5
Substitute each letter by a different digit from 0 to 9 to satisfy this alphanumeric multiplication problem.


Note: Neither V nor T can be 0.

See The Solution Submitted by K Sengupta    
Rating: 3.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(2): Solution | Comment 3 of 4 |
(In reply to re: Solution by Josie Faulkner)

The assumption, in most cases, is that we are restricted to decimal numbers (base 10).  As I enjoy looking for solutions that may be other than those that are assumed, I looked at the other bases for possible solutions. 
Given five different letters, the minimal base would be base 5.  A solution of base 9 or less would limit the digits the solution could have, yet any such solution would still satisfy that the digits involved are within the set of digits 0 to 9.
The maximum base would be where the square of a three digit can produce a 6-digit number is base 82.  All squares of three digit numbers of a given radix larger than 82 are less than six digits. 
As it is, of each of these bases, only base 10 produces a result where the digits of VELVET and TIE are different digits 0 to 9. And, in base 10, only one solution exists, therefore the solution is unique.

  Posted by Dej Mar on 2008-02-26 00:27:31
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