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

Home > Numbers
1 to 9 concatenation (Posted on 2016-04-12) Difficulty: 3 of 5
What is the largest number n so that n, 2n, and 3n together contain every digit from 1-9 exactly once?

Analytical solution preferred.

No Solution Yet Submitted by Ady TZIDON    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
A start | Comment 3 of 7 |
A few observations

a) n must be three digits.  Two digits is too little and 4 are too many.

b) n must be greater than 123.

c) n must be less than 330.  Otherwise, either digits are repeated or 3n has 3 digits.

d) if n, 2n and 3n contain all digits, then their sum of digits = 45, so the sum is divisible by 9.
   but the sum = 6n, so n must be divisible by 3.
   
d) So, that leaves less than 70 that might work   

  Posted by Steve Herman on 2016-04-12 12:19:59
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 (6)
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