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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)

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re(4): computer solution ?????? | Comment 6 of 7 |
(In reply to re(3): computer solution ?????? by Ady TZIDON)

  n(1) = a + b + c + d
  n(2) = e + f + g + h
  n(3) = i + j + k + l
  n(4) = m + n + o + p
  n(5) = a + e + i + m
  n(6) = b + f + j + n
  n(7) = c + g + k + o
  n(8) = d + h + l + p
  n(9) = a + f + g + h
  n(10) = d + g + j + m
 
  should have been
 
  n(1) = a + b + c + d
  n(2) = e + f + g + h
  n(3) = i + j + k + l
  n(4) = m + n + o + p
  n(5) = a + e + i + m
  n(6) = b + f + j + n
  n(7) = c + g + k + o
  n(8) = d + h + l + p
  n(9) = a + f + k + p
  n(10) = d + g + j + m
 
  (the n(9) set typed wrong)
 
replacement set:
  1  2  3  4
  5  6  7  8
  9 10 11 12
 13 14 16 15   10  26  42  58  28  32  37  39  33  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  32  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  34  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  33  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  31  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  34  36
  1  2  3  4
  5  6  7  8
  9 10 11 12
 15 13 16 14   10  26  42  58  30  31  37  38  32  36
  1  2  3  4
  5  6  7  8
  9 10 11 12
 15 16 14 13   10  26  42  58  30  34  35  37  31  36
  1  2  3  4
  5  6  7  8
  9 10 11 12
 16 14 13 15   10  26  42  58  31  32  34  39  33  37

 

  Posted by Charlie on 2011-07-13 11:41:12
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