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

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

How many of these integers are palindromes? How many are tautonymic numbers?

Note:
A tautonymic number is one which can be divided into two equal non-palindromic halves, with each part having at least two different digits. For example, each of 3636, 5252, 6767, 276276 and 56635663 is a tautonymic number - but, none of 4444 and 555555 is a tautonymic number.

A quick run thru with Mathematica gave the following Palindromes

(1^5/2)+(3^7/6)+(4^9/3)=33133

(2^5/1)+(3^7/9)+(4^6/2)=787

(2^5/4)+(3^8/1)+(6^7/3)=37673

(3^8/9)+(5^7/2)+(6^1/3)=39793

(4^7/8)+(5^3/2)+(9^1/3)=2112

(7^5/2)+(8^4/1)+(9^3/3)=12621

and for the lone tautonymic number

(2^5/8)+(3^7/9)+(4^6/3)=4343

Posted by Daniel on 2009-03-03 13:29:50