RAJ

how many squares?


The answer is 40.

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2 solutions

Anuj Shikarkhane
Jul 10, 2014

This is a 4 by 4 grid. So the number of squares is 4 × 4 + 3 × 3 + 2 × 2 + 1 × 1 = 30 4\times4 + 3\times3 + 2\times2 + 1\times1 = 30 (excluding the 2 squares in the middle)

Now look at the two big squares in the centre.

Therefore, number of squares in the first square is 2 × 2 + 1 × 1 = 5 2\times2 + 1\times1 = 5

There are two such squares.

Hence, total squares are 5 × 2 = 10 5\times2 = 10

So total number of squares in this figure should be 30 + 10 = 40. 30 + 10 = 40.

(Kindly up vote if you liked this)

Palash Som
Nov 4, 2014

simple formula to apply is (n n+1 *2n+1) /6 for n n sides of a square then the 2 squares in the n*n sides square can be added hence answer is 40\

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