7. On the blackboard is a 3×3 magic square. The sum of the three numbers in each
row, each column and each diagonal is the same. As shown in the diagram below,
all but three of the numbers are erased. What is the number represented by x in
the cell at the upper left corner?
x 21 94
3
【Solution】
Label some of the other numbers as shown in the right diagram.
Then 94+21+x=x+3+z so that z=112.
3 y
From 94+21+x=21+y+a, a−x=94−y.
From x+y+b=112+a+b, a−x=y−112.
z a b
Hence 94−y=y−112 so that y=103.
From 94+21+x=94+103+112, x=194.
ANS: 194
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