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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 Parametric solutions | Comment 4 of 5 |
Jer noted "If r is not zero, r+r has a carry so for e+e to end in r, r must be odd."  When this is true then the base x is of the form 4y+2.

Then starting with y=4, the following parametric solution finds a solution for every base 18,22,26,30,....
B=y-1, E=y, G=1, I=4y-1, M=4y+1, N=4y, R=2y+1, T=2, U=4y-2

4y-1 4y      2  y      1  y   2y+1
+ 4y 4y-2 4y+1 y-1 y 2y+1
4y 4y-2 4y+1 y-1 y 2y+1 0

  Posted by Brian Smith on 2016-12-19 13:59:26
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