Magic square - 1.0
The figure below shows a
magic square.
Which of the following statements is/are true?
A : It is possible that ( ) are in some order.
B : It is possible that ( ) are in some order.
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1 solution
A : The sum of the numbers is 2 9 , which is not divisible by 3 . Since the 2 , 2 , 3 , 3 , 3 , 4 , 4 , 4 , 4 numbers are intgeres, it is not possible.
B : Suppose yes. Then a + b + c = d + e + f = g + h + i = a + d + g = b + e + h = c + f + i = 3 0 + 1 + 2 + 4 + 5 + 7 + 8 + 1 0 + 1 1 = 1 6 . It is celar that since 1 0 + 1 1 > 1 6 , 1 0 and 1 1 can't be in the same row or in the same column. There are two ways to add two numbers to 1 1 to get 1 6 : 1 6 = 1 1 + 0 + 5 and 1 6 = 1 1 + 1 + 4 . There are two ways to add two numbers to 1 0 to get 1 6 : 1 6 = 1 0 + 1 + 5 and 1 6 = 1 0 + 2 + 4 . But 2 and 4 can't be in the same row/column, which is contradiction. So it is impossible.
Therefore neither of them is possible.