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.

The lowest solution would be WELL = 2899 for:

x=12 (x**4=20736)

y=13 (y**4=28561)

z=14 (z**4=38416)

y**4 - x**4 = 7825 = NEWS

z**4 - y**4 = 9855 = LESS

WELL = 2899

I have tested on x,y,z less than 100.  I will expand the code to see if there are higher values.

Posted by ed bottemiller on 2009-04-15 12:43:20