All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Numbers
Elegant Exponent Exposition II (Posted on 2010-12-04) Difficulty: 3 of 5
Each of the capital letters in bold denotes a different base ten digit from 1 to 9 in this cryptarithmetic expression:

                                         AB/C + DE/F + GH/I

(I) Determine the respective smallest and the largest positive integer that this expression can assume.

(II) Determine the respective smallest and the largest prime number that this expression can assume. What are the respective smallest and the largest palindrome assumed by the above expression?

No Solution Yet Submitted by K Sengupta    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution re: computer solution for integers and primes -- now palindromes | Comment 2 of 3 |
(In reply to computer solution for integers and primes by Charlie)

the added code:

100           :spal=cutspc(str(sum))
110           :pal=1
120           :for i=1 to int(len(spal))
130              :if mid(spal,i,1)<>mid(spal,len(spal))+1-i,1) then pal=0:endif
140           :next
150           :if pal=1 and sum<lowpal then lowpal=sum:lowpalstr=s$:endif
155           :if pal=1 and sum>highpal then highpal=sum:highpalstr=s$:endif

finds

157263948        8
693742851        33033

where 693742851 represents 6^(9/3)+7^(4/2)+8^(5/1), which equals the largest palindrome: 33033.


  Posted by Charlie on 2010-12-04 19:55:33
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information