Square-ception

How many squares are there in the image?


The answer is 10.

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12 solutions

Lohit Jain
Aug 6, 2014

There's the largest square: 1.
There's the green square: 1.
The green square splits into 4 green squares: 4.
There's 4 squares: top left, top right, bottom left, bottom right.


So there's a total of 1 + 1 + 4 + 4 = 10 1+1+4+4 = 10 squares.

The given image is a 2×2 grid with small 2×2 grid at the middle. To get the no. of squares in a 2×2 grid, add the sum of the squares of 1 and 2 i.e 1^2 + 2^2 = 1+ 4= 5 Since there is another 2×2 grid at the middle multiply 5 by 2 Therefore, there are 10 squares.

Another solution 2(1^2 + 2^2) = 2(5) =10 squares

Wangsky Wangers - 5 years, 8 months ago

One big + one small + 4 square parts of the big square & 4 square parts in the small square.

Saleemddin Mulla - 6 years, 10 months ago
Desiree Guasch
Aug 7, 2014

4 yellow & green squares + 4 small green squares + 1 big green square + 1 biggest yellow & green square

Andrew Tawfeek
Feb 8, 2016

Bonus question: How many quadrilaterals are in the image

18 quadrilaterals Two lines are dividing yellow square in two rectangles each, so there are 4 yellow rectangles. Same with green square. There are 10 squares and 2*4 rectangles, so in total 18 quadrilaterals.

Raghav Kabra - 2 years, 7 months ago
Don Weingarten
Feb 3, 2019

The large square The green central square The four squares into which the green square is divided. The four squares into which the large square is divided 4+4+1+1 = 10

Wangsky Wangers
Oct 6, 2015

The given image is a 2×2 grid with small 2×2 grid at the middle. To get the no. of squares in a 2×2 grid, add the sum of the squares of 1 and 2 i.e 1^2 + 2^2 = 1+ 4= 5 Since there is another 2×2 grid at the middle multiply 5 by 2 Therefore, there are 10 squares.

Another solution 2(1^2 + 2^2) = 2(5) =10 squares

Sherilynne Ruiz
Sep 29, 2015

The whole square, the whole green square , and the divided yellow and green square..

Kevin Dheer
Jan 2, 2015

5 of the green ones ( 4 inner, 1 whole )and 5 of the brown ones( 4 inner, 1 whole)

Jonah Shader
Nov 3, 2014

count the lines. they add up to 10.

Gini Mas
Aug 9, 2014

The 8 directly visible, as well as the square as a whole and the green square formed by the 4 small squares. 10.

Krishna Garg
Aug 7, 2014

Inside as well out side will have 5 each ,so total 10 Ans K.K.GARG,India

Answer by Krishna

Muhammad Adeel - 6 years, 10 months ago
Suraj Sharma
Aug 7, 2014

1 exterior,4pieces of the outer one,1inner and 4 pieces of the inner one

Madiha Javid
Aug 6, 2014

1 big square divided into 4 smaller squares making a total of 5. 1 central smaller square divided into 4 even smaller ones making another total of 5. Together they make 10.

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