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Palindromic and Tautonymic II (Posted on 2009-12-20) Difficulty: 3 of 5
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?

No Solution Yet Submitted by K Sengupta    
Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution computer solution to part I | Comment 1 of 4
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
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