Given a list of positive integers a, b, c, ... z, you can calculate the superpower a^b^c^...^z. [Note that this is a^(b^(c^(...(y^z)...))).]

What's the largest/least superpower value you can get with the list 2, 3, 4, ... n?

(In reply to Intuitive guess by Cory Taylor)

For the set 2,3,4 the greatest superpower occurs with 2^(3^4) but the smallest is 4^(2^3).  My guess is that ascending order yields the greatest result and decending order with the last two digits being 2 then 3 (since 2^3 < 3^2) yeilds the smallest result.  I think that the 2,3 pair at the end is the only anomoly (also of note is the fact that 2^4 = 4^2)

Edited on April 4, 2005, 8:41 pm

Posted by Eric on 2005-04-04 20:32:08