Magic Sum 1

Algebra Level 3

Find the sum of all numbers which are to be put into a magic square whose magic sum is 369.

This problem is part of the set Magic Squares Mania .

The answer is 3321.

1 solution

Arya Samanta
May 13, 2014

Well You gotta be aware MAgIC SQuaRes.. but I found this one as I thought it to be a $9 \times 9$ grid.(i.e. a magic square of order 9)

And luckily it came to be the RIGHT!!

So if a single ROW has sum $=369$ , hence the whole square[ $9 \times 9$ ] will have

$\Rightarrow$ THE SUM $=9 \times 369$

$\Rightarrow$ WHICH IS $=\boxed{3321}$

Yours friendly

Arya :)

Nice intuition, Arya. :D

But to formalize the solution, one method is to show first that the magic sum of a magic square of order $n$ is $\frac{n}{2}(n^2+1)$ . Then equate it to 369 to solve for $n$ (which happens to be $n=9$ ). Thus there will be 81 numbers (from 1 to 81), and thus the sum of these numbers will be $\frac{81}{2}(1+81)=3321.$

Jaydee Lucero - 7 years, 1 month ago

Magic Sum 1

The answer is 3321.

1 solution

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