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Sum number equals integer (Posted on 2011-06-11) Difficulty: 3 of 5
Each of the small letters in bold represents a different base x digit from 0 to x-1 to satisfy this alphametic equation. None of the numbers can contain any leading zero.

                              (x-1)*number = integer

Determine the minimum positive integer value of x such that the above equation has at least one solution. What is the next smallest value of x having this property?

No Solution Yet Submitted by K Sengupta    
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Solution re: Parametric solutions - Improved Comment 5 of 5 |
(In reply to Parametric solutions by Brian Smith)

Let z=x/2.  Then a parametric solution for all even bases starting with x=14 is:

B=z-2, E=z, G=1, I=2z-4, M=2z-2, N=2z-3, R=0, T=3, U=2z-6
2z-4 2z-3    3  z     1 z 0
+ 2z-3 2z-6 2z-2 z-2 z 0
2z-3 2z-6 2z-2 z-2 z 0 0

  Posted by Brian Smith on 2016-12-21 12:18:56
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