x, y and z (in this order), with x < y < z, are three positive integers in arithmetic sequence that satisfy this set of alphametic equations.

y⁴ - x⁴ = NEWS, and

z⁴ - y⁴ = LESS.

where, each of the capital letters in bold represents a different decimal (base 10) digit from 0 to 9.

Determine all possible value(s) of the triplet (x, y, z).

What are the possible four digit number(s) that represent WELL?

Note: Neither L nor N is zero.

(In reply to all's well that ends well by ed bottemiller)

I took a slightly different approach, I went through all possible alphametic values for NEWS,LESS and then seen which give integer solutions to y^4-x^4=news z^4-y^4=less and z=2y-x with x>0 and y>x.  I found only one solution which matches your own of x=12 y=13 and z=14.

Posted by Daniel on 2009-04-15 13:03:21