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.

I'm glad to see we reached the same result.  I was a bit concerned that W might be zero (puzzle does say WELL is a four-digit number, but of course for the cases of NEWS and LESS the text added the constraint/interpretation that neither N nor L were zero.  I expanded my test for x,y,z up to 1000 but found no others; probably wasted effort since the difference between two consecutive fourth powers soon exceeds 9999 in any case .  I wonder why the puzzle said to "determine all possible value(s) of the triplet" if the solution we found is unique.

 

Posted by ed bottemiller on 2009-04-15 14:00:52