Problem Background : A 4x4 magic square is an arrangement of 16 squares arranged in 4 rows and 4 columns. We are given 16 terms in an arithmetic progression(AP) to place in each of the squares such that the sum of each of the rows and columns is equal.
Solution : We assume the terms of the AP are a,a+d,a+2d,...,a+14d,a+15d where a is the first term and d is the common difference.
© Rishabh Bidya
Solution : We assume the terms of the AP are a,a+d,a+2d,...,a+14d,a+15d where a is the first term and d is the common difference.
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| General Solution of a 4x4 magic square |
Derived corollary : It can be noted that we get a magic square of any 16 consecutive integers when d=1 and a is the first term among the 16 integers.
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| Magic square of any 16 consecutive integers where a is the first integer |
Example: If a=1 and d=1, we get a magic square of the integers from 1 to 16.
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| Magic square of first 16 natural numbers |
Q.E.D
© Rishabh Bidya
