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?

Creating a program to check all possible combinations of A-I, gets us a list of 209 possible distinct positive palindromes. Our minimum palindrome is 1:

1 : A=1, B=2, C=3, D=4, E=6, F=8, G=7, I=5
1 = (1-2)^3 + (3-4)^6 + (8-7)^5

Our maximum occurs once:

5764675 : A=1, B=6, C=3, D=4, E=5, F=2, G=9, I=8
5764675 = (1-6)^3 + (3-4)^5 + (2-9)^8 = -125 + -1 + 5764801

As for the 2nd part of the problem dealing with tautonymic numbers, I'll look into it later, but I don't have the time to do so right now.

Posted by Justin on 2009-12-20 14:03:45