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

Home > Just Math
Nondivisibility by 11 (Posted on 2017-08-06) Difficulty: 2 of 5
The number 545 has the curious property that — after replacing any single digit by another arbitrary digit (from 0 to 9; it can be a leading 0 or just the same digit) — the result is not divisible by 11.

Is there a positive integer with this property having an even number of digits?

No Solution Yet Submitted by Danish Ahmed Khan    
Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Solution and more | Comment 1 of 2
First, why does 545 have this property?  (5+5)-(4)=6.  Which needs to become either 0 or 11.  Changing a 5 can increase this by up to 4 or decrease by 5.  Changing the 4 can only do the same.  So the 6 (mod 11) is the important difference if we are going to have a number composed of alternating 5's and 4's.  

545454545454 has the property and has 12 digits as does its reverse.

5454545454545454545454545 has 17.

You can also append or 454545454 to these.

Is there a number not composed of alternate 4's and 5's?  Yes, but I overlooked them.  See Brian Smith's Solution.

Edited on August 6, 2017, 2:41 pm
  Posted by Jer on 2017-08-06 09:24:22

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