Φ, Γ and Λ (in this order) with Φ < Γ < Λ are three positive integers in arithmetic sequence that satisfy this set of alphametic equations:

Λ³ - Γ³ = TWO, and:

Γ³ - Φ³ = TOW

where each of the letters T, O and W represent a different decimal (base 10) digit from 0 to 9.

What are the possible value(s) of the triplet (Φ, Γ, Λ)?

Note: T is not zero.

** Can you do this in a short time, using pen and paper, and eventually a hand calculator, but no computer programs?

(In reply to Solution by Praneeth)

Thanks, Praneeth.

I confirm having hyperlinked your methodology in my solution.

Posted by K Sengupta on 2008-07-16 06:23:12