SOLUTION: AGENT 86 Fill in the missing square in such a way that the rows, columns, and diagonals all add up to the same number. 32 19 ___ 8 10 25 ___ ___ 9 ___ ___

Algebra ->  Sequences-and-series -> SOLUTION: AGENT 86 Fill in the missing square in such a way that the rows, columns, and diagonals all add up to the same number. 32 19 ___ 8 10 25 ___ ___ 9 ___ ___       Log On


   

Question 722803: AGENT 86
Fill in the missing square in such a way that the rows, columns, and diagonals all add up to the same number.
32 19 ___ 8
10 25 ___ ___
9 ___ ___ ___
35 16 ___ 11
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
32 19  A  8
10 25  B  C
 9  D  E  F
35 16  G 11

The 1st column going down is 32+10+9+35 = 86

So all the rows, columns and the two diagonals 
must have sum 86

The first row going across is 32+19+A+8 = 86
                                   59+A = 86
                                      A = 27

32 19 27  8
10 25  B  C
 9  D  E  F
35 16  G 11

The 2nd column going down is 19+25+D+16 = 86
                                   60+D = 86
                                      D = 26

32 19 27  8
10 25  B  C
 9 26  E  F
35 16  G 11

The bottom (4th) row going across is 35+16+G+11 = 86
                                           62+G = 86
                                              G = 24

32 19 27  8
10 25  B  C
 9 26  E  F
35 16 24 11 



The diagonal from upper left to lower right is

                             32+25+E+11 = 86
                                   68+E = 86
                                      E = 18

32 19 27  8
10 25  B  C
 9 26 18  F
35 16 24 11

The 3rd column going down is 27+B+18+24 = 86
                                   69+B = 86
                                      B = 17

32 19 27  8
10 25 17  C
 9 26 18  F
35 16 24 11

The 2nd row going across is 10+25+17+C = 86
                                  52+C = 86
                                     C = 34

32 19 27  8
10 25 17 34
 9 26 18  F
35 16 24 11

The 3rd row going across is 9+26+18+F = 86
                                 53+F = 86
                                    F = 33

32 19 27  8
10 25 17 34
 9 26 18 33
35 16 24 11

Edwin