Consider this calendar. Select the numbers 1,2,3,8,9,10,15,16,17 such that they form a square. The sum of the selected numbers of the square, is ____ times the middle number of the square.

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Solution

The correct option is D
9

Sum of the selected numbers
= 1 +2 + 3+ 8 + 9 + 10 + 15 +16 +17
= 81

If the central number is x, we can fill in the other numbers in the way displayed above.

Sum of these numbers would be
= x - 8 + x - 7 + x - 6 + x - 1 + x + x + 1 + x + 6 + x + 7 + x + 8
= 9x

Hence, sum of all the 9 numbers = 9 times the central number.

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