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.
(AB)^{C} + (CD)^{E} + (FG)^{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 AI, 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=51 = (12)^3 + (34)^6 + (87)^5
Our maximum occurs once:
5764675 : A=1, B=6, C=3, D=4, E=5, F=2, G=9, I=85764675 = (16)^3 + (34)^5 + (29)^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 20091220 14:03:45 