Make a list of distinct positive integers that are obtained by assigning a different base ten digit from 1 to 9 to each of the capital letters in this expression.

(A-B)^C + (C-D)^E + (F-G)^I

What are the respective minimum and maximum positive palindromes from amongst the elements that correspond to the foregoing list.

As a bonus, what are the respective minimum and maximum positive tautonymic numbers that are included in the list? How about the respective maximum and minimum negative tautonymic numbers?

The lowest, or most negative, palindrome I found is (4-6)^5 + (5-9)^1 + (2-8)^7 = -279,972.  The highest, or least negative, is of course -1, with (1-2)^3 + (3-4)^5 + (6-7)^8 as one way to get it.

The lowest tautonymic I found is (1-4)^6 + (6-8)^3 + (2-9)^7 = -822,822.  And for the highest tautonymic, one of several ways to get -1010 is (2-6)^5 + (5-3)^4 + (7-9)^1.

Looking at the earlier Palindromic and Tautonymic problem, I can't help but wonder if the equation for this problem should really be (A-B)^C + (D-E)^F + (G-H)^I, and it would be interesting to see what the results of that would be ...

Posted by Jim Keneipp on 2009-12-20 19:14:09