Question

When certain numbers are placed in the empty boxes, the sum of each of the three numbers in the three rows, three columns, and two diagonals is the same. What number should be in the center box?

Answer 1

Given :  certain numbers are placed in the empty boxes

the sum of each of the three numbers in the three rows, three columns, and two diagonals is the same.

To Find :  number  in the center box

Solution:

5            A            13

B           C             D

9           7              E

5 + A + 13  = 5 + B + 9

=> A + 18 = B + 14

=> A + 4 = B

=> B = A  + 4

5 + B + 9  =  9 + 7  + E

=> 14 + B = 16 + E

=> E  = B - 2

=> E = A +4 - 2

=> E  = A  + 2

5 + A + 13  = 13 + D + E

=>  5 + A  = D + E

=> 5 + A = D + A + 2

=> D = 3

 5            A            13

A+4        C             3

9             7             A + 2

5 + A + 13  = A + 4 + C + 3

=> C = 11

 5            A            13

A+4        11             3

9             7             A + 2

Hence number 11 should be in the center box

9 + 11 + 13  = 33

18 + A  = 33

=> A = 15

                                       = 33

5           15           13         = 33

19          11            3         = 33

9            7            17       = 33

=             =             =       = 33

33          33           33

Number in the center box  = 11

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