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

Home > Probability
Antimagic square (Posted on 2011-07-12) Difficulty: 4 of 5
Let us place at random the digits from 1 to 9 into the cells of 3x3 square.
What is the probability of getting a configuration such that the 8 sums (3 rows, 3 columns and 2 main diagonals) will be represented by 8 distinct numbers?
Construct at least one such square.

Extra challenge:
Same two tasks for 4x4 square , numbers 1 to 16 and 10 distinct sums.

No Solution Yet Submitted by Ady TZIDON    
Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(2): computer solution | Comment 4 of 7 |
(In reply to re: computer solution by Ady TZIDON)

samples of 4x4

 1  2  3  4
 5  6  7  8
 9 10 11 12
13 14 15 16   10  26  42  58  28  32  36  40  22  34
 1  2  3  4
 5  6  7  8
 9 10 11 12
13 14 16 15   10  26  42  58  28  32  37  39  22  34
 1  2  3  4
 5  6  7  8
 9 10 11 12
13 15 14 16   10  26  42  58  28  33  35  40  22  34
 1  2  3  4
 5  6  7  8
 9 10 11 12
13 15 16 14   10  26  42  58  28  33  37  38  22  34
 1  2  3  4
 5  6  7  8
 9 10 11 12
14 13 15 16   10  26  42  58  29  31  36  40  22  35
 1  2  3  4
 5  6  7  8
 9 10 11 12
14 13 16 15   10  26  42  58  29  31  37  39  22  35
 1  2  3  4
 5  6  7  8
 9 10 11 12
14 15 13 16   10  26  42  58  29  33  34  40  22  35
 1  2  3  4
 5  6  7  8
 9 10 11 12
14 16 15 13   10  26  42  58  29  34  36  37  22  35
 1  2  3  4
 5  6  7  8
 9 10 11 12
15 13 14 16   10  26  42  58  30  31  35  40  22  36

  Posted by Charlie on 2011-07-12 23:26:38
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 (7)
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