72-Magic Square-5 (different cells and addition part-2)

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Addition of different cell elements of Magic Squares:

We have seen the addition of the elements in rows columns, and diagonals are the same in all the cases. Each row or column or diagonal contains 4 elements. Now we see the elements in different cases or places will also show the addition as 34.

The following diagram gives us the details of all possible 4 places or cells which we are considering as our elements.

 (1 + 15 + 12 + 6)      (14 + 4 + 7 + 9)

(R₁C₁, R₁C₂, R₂C_1, R₂C₂)    (R₁C₃, R₁C₄, R₂C_3, R₂C₄)

Here the Sum of all these numbers is 34 (1 + 15 + 12 + 6). In the same way, we can observe the same sum for all other diagrams.

Now we will see the remaining groups of different places of cells taken into account to get the sum as 34

 

(11 + 5 + 2 + 16)      (8 + 10 + 13 + 3)

(R₃C₃, R₃C₄, R₄C_3, R₄C₄)  (R₃C₁, R₃C₂, R₄C_1, R₄C₂)

(15 + 14 + 3 + 2)      (8 + 12 + 9 + 5)

(R₁C₂, R₁C₃, R₄C_2, R₄C₃)  (R₂C₁, R₃C₁, R₂C_4, R₃C₄)

(15 + 12 + 5 + 2)      (14 + 9 + 8 + 3)

(R₁C₂, R₂C₁, R₃C_4, R₄C₃)  (R₁C₃, R₂C₄, R₃C_1, R₄C₂)

(6 + 7 + 10 + 11)         (1 + 4 + 13 + 16)

(R₂C₂, R₂C₃, R₃C_2, R₃C₃)  (R₁C₁, R₁C₄, R₄C_1, R₄C₄)

(1 + 7 + 10 + 16)         (4 + 6 + 11 + 13)

(R₁C₁, R₂C₃, R₃C_2, R₄C₄)  (R₁C₄, R₂C₂, R₃C_3, R₄C₁)

(6 + 9 + 3 + 16)         (15 + 4 + 10 + 5)

(R₂C₂, R₂C₄, R₄C_2, R₄C₄)  (R₁C₂, R₁C₄, R₃C_2, R₃C₃)

(12 + 7 + 13 + 2)         (1 + 14 + 8 + 11)

(R₂C₁, R₂C₃, R₄C_1, R₄C₃)  (R₁C₁, R₁C₃, R₃C_1, R₃C₃)
Like this, you can also find so many relations between the numbers reflected in cells and their addition.

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ANIL SATPUTE