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

Home > Just Math
50 - Digit Number (Posted on 2003-11-15) Difficulty: 3 of 5
A number of 50 digits has all its digits equal to 1 except the 26th digit. If the number is divisible by 13, then find the digit in the 26th place.

See The Solution Submitted by Ravi Raja    
Rating: 3.3333 (6 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: solution | Comment 18 of 39 |
(In reply to solution by Charlie)

Your observation about the powers of 10 mod 13 leads to the conclusion that replacing the powers of 10 by their mod 13 equivalents gives 4*0+10*x+1+4*0 as a mod 13 representation of the 50-digit number since 1+10+9+12+3+4=39 is divisble by 13. Now 10*x+1 is divisble by 13 if x=9, and one may readily check by brute force that 91 is the only two-digit number that ends in 1 and is divisible by 13. Hence x=9 uniquely renders the 50-digit number divisble by 13 as desired.
  Posted by Richard on 2003-11-20 20:35:49

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 (2)
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