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?

OK, I ran the numbers for the 9-variable equation (A-B)^C + (D-E)^F + (G-H)^I and got the following results:

Palindromes:  Highest was 5,764,675 = (1-6)^3 + (2-9)^8 + (4-5)^7; lowest was -97,097 = (1-4)^6 + (2-5)^9 + (3-8)^7.

Tautonyms:  Highest was only 7272 = (2-4)^9 + (7-1)^5 + (8-6)^3; lowest was only -7272 = (1-7)^5 + (2-4)^3 + (8-6)^9.  Of note, no results came up for -1010 this time, although I did find that -1919 = (1-4)^7 + (3-8)^2 + (9-6)^5 -- so a less negative result is still possible.

Posted by Jim Keneipp on 2009-12-21 04:22:40