Magic Square!

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The above 3 3 by 3 3 square have letters A to I. Substitute these letters with numbers 1 1 through 9 9 without repeitition such that all their rows, columns, and diagonals adds up to the same value.

Let

a a denote as the value of the sum of each row, column, or diagonal,

b b denote as the value of the middle number (i.e. E),

c c denote the sum of the four corner numbers.

Evaluate a + b + c a+b+c

Picture Source File: 3 by 3 square

21 40 45 35 25

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Chester Robinson by Chester Robinson , 25, United Kingdom

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1 solution

Roman Frago
Mar 3, 2015

A + B + C + D + E + F + G + H + I = 45 A+B+C+D+E+F+G+H+I=45

a = A + B + C = D + E + F = G + H + I a=A+B+C=D+E+F=G+H+I

3 a = 45 ; a = 15 3a=45;a=15

A + E + I + B + E + H + C + E + G + D + E + F = 4 a A+E+I+B+E+H+C+E+G+D+E+F=4a

A + B + C + D + 4 E + F + G + H + I = 60 A+B+C+D+4E+F+G+H+I=60

45 + 3 E = 60 ; E = 5 ; b = 5 45+3E=60;E=5;b=5

c = A + C + G + I c=A+C+G+I

c = 45 − ( B + E + H + D + F ) c=45-(B+E+H+D+F)

c = 45 − 2 a + E = 20 c=45-2a+E=20

a + b + c = 15 + 5 + 20 = 40 a+b+c=15+5+20=40

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