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.
(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
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Posted by Charlie
on 2011-07-12 23:26:38 |
re(2): computer solution
