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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 3 of 7 |
(In reply to re: computer solution by Ady TZIDON)

Some samples with the totals:

 1  2  3
 4  5  8
 6  9  7       6  17  22  11  16  18  13  14

 1  2  3
 4  5  9
 6  8  7       6  18  21  11  15  19  13  14

 1  2  3
 4  5  9
 7  6  8       6  18  21  12  13  20  14  15

 1  2  3
 4  6  7
 9  8  5       6  17  22  14  16  15  12  18

 1  2  3
 4  6  8
 5  7  9       6  18  21  10  15  20  16  14

 1  2  3
 4  7  8
 5  9  6       6  19  20  10  18  17  14  15

 1  2  3
 4  7  9
 5  8  6       6  20  19  10  17  18  14  15

 1  2  3
 4  8  5
 7  9  6       6  17  22  12  19  14  15  18

 1  2  3
 4  8  9
 6  5  7       6  21  18  11  15  19  16  17

 1  2  3
 4  9  8
 7  6  5       6  21  18  12  17  16  15  19

 1  2  3
 5  6  7
 8  4  9       6  18  21  14  12  19  16  17


  Posted by Charlie on 2011-07-12 23:15:35
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