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Powerful Powers Pileup! (Posted on 2005-04-03) Difficulty: 3 of 5
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?

See The Solution Submitted by Old Original Oskar!    
Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Intuitive guess | Comment 2 of 3 |
(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

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