Substitute each letter by a different digit from 0 to 9 to satisfy this alphanumeric multiplication problem.
VELVET = (TIE)*(TIE)
Note: Neither V nor T can be 0.
(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