Magic square

I hope you all know what magic squares are.

If a 5 × 5 5\times 5 magic square is made as shown, then what will be the sum of the values at the places given in the figure?


The answer is 169.

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2 solutions

Akshat Sharda
Jul 11, 2015

Making a magic square of 5 × 5 5×5 : S t e p 1 Step 1 Write all number till 5 2 5^{2} .

S t e p 2 Step 2 Arrange them like this.

S t e p 3 Step 3

S t e p 4 Step 4 Place the pink one like this and do the same for other three corners.

S t e p 5 Step 5 You are done !!

This will work for all odd numbered magic squares.

Now the sum, = 3 + 9 + 15 + 8 + 14 + 7 + 13 + 19 + 12 + 18 + 11 + 17 + 23 = 3+9+15+8+14+7+13+19+12+18+11+17+23 = 169 = \boxed{169}

Moderator note:

Is it a coincidence that the answer is 1 3 2 13^2 ?

Saya Suka
Dec 9, 2016

You do not need to know how they are arranged in the magic square to know the answer. There is a formula to get the answer for any odd sided magic square alternate sum that include the central square, and that is [(m^2+1)/2]^2 for all odd m-sided magic squares. So for m=5, answer equal ((5^2+1)/2)^2 = ((25+1)/2)^2 = 13^2 = 169.

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