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

Home > Numbers
Extreme Eleven Exercise (Posted on 2010-01-21) Difficulty: 3 of 5
N is an 11-digit base ten prime number N (with no leading zero) with the proviso that N contains each of the digits from 0 to 9 at least once.

Determine the respective minimum and maximum value of N.

No Solution Yet Submitted by K Sengupta    
Rating: 3.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Answers | Comment 3 of 4 |

In order to fail the divisibility test for 9 with the proviso that each of the digits from 0 to 9 occur at least once, the smallest additional digit is 1 and the largest additional digit is 8:
9+8+7+6+5+4+3+2+1+0+0 = 45 => 45 is divisible by 9,
9+8+7+6+5+4+3+2+1+0+9 = 54 => 54 is divisible by 9.

In addition, non-single digit primes must end with one of the four odd digits: 1, 3, 7 or 9.

Thus, one can begin with the 11-digit base ten pandigital number 10123456789 and proceed to higher numbers to find
the smallest 11-digit base ten pandigital prime to be 10123457689.
And, one can begin with the 11-digit base ten pandigital number 98876543201 and proceed to lower numbers to find
the largest 11-digit base ten pandigital prime to be 98876532401.


  Posted by Dej Mar on 2010-01-21 16:54:16
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 (10)
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