How Many Squares
How many Squares in this picture #2
You might want to try How many squares – Part 1 before you attempt these 3 puzzles.
You might want to try How many squares – Part 1 before you attempt these 3 puzzles.
How?
Let say smallest square is of side 1cms then
Number of squares with side 1cms: 6
Number of squares with side 2cms: 8
Number of squares with side 3cms: 2
Number of squares with side 4cms: 1
How?
Lets assume smallest square side length is 0.5 cms, then
Number of squares with side 0.5 cms: 30
Number of squares with side 1 cms: 16+11
Number of squares with side 1.5 cms: 2 + 3 + 2
Number of squares with side 2 cms: 9 + 1
Number of squares with side 2.5 cms: 0
Number of squares with side 3 cms: 4
Number of squares with side 3.5 cms: 0
Number of squares with side 4 cms: 1
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Thus total number of squares are: 79
As all the sides are either horizontal or vertical we can say squares diagonals should be parallel. Now to see if the diagonals are parallel or not, i have drawn the diagonals where its not clear if it is a square or rectangle in the image below.
You can see i have labelled few sides as x and y to help you.
So,
Number of squares with side x/2 = 4
Number of squares with side x = 4
Number of squares with side y = 3
Number of squares with side x+y = 6
Number of squares with side x+y = 0
Number of squares with side x+2y = 1
Number of squares with side 2x+2y = 1
How?
Lets Count..
5 black colored squares.
1 red colored square.
1 blue color square.
4 small green colored squares in middle.
5 large green colored squares.
Thus, a total of 5+1+1+4+5=16 squares.
1.)
See AnswerHide AnswerHow?
Let’s assume the smallest square side is 0.5cm in length.
Now count the squares with different length :-
0.5cm : 8
1cm : 16 +2(in the middle)
2cm : 9
3cm : 4
4cm : 1
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Total : 40
Lets count…
Squares with side length equal to 1 matchstick: 9
Squares with side length equal to 2 matchsticks: 5(2+1+2)
Square with side length equal to 3 matchsticks: 1 (This is difficult to find, and easy to miss)
Square with side length equal to 4 matchsticks: 1 (Everybody knows)
So total number of squares : 16
This image(courtsey Charles on facebook) explains it all:-