Find the number of shapes in the following figure.
A shape is something that consists of exactly one simple circuit.
For example, in the following figure, there are 6 figures.
They are :-
1)
2)
3)
4)
5)
6)
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First let us consider 1 circle:-
There is only
1
shape.
Now, consider 2 circles
There are
6
shapes
Now consider 3 circles.
There are
1
5
shapes
Now consider 4 circles
There are
2
8
shapes.
Now consider 5 circles
There are
4
5
shapes
Now consider 6 circles.
There are
6
6
shapes.
So, we observe that in no. of shapes in case 2 is 5 more than that in case 1
No. of shapes in case 3 is 5 + 4 = 9 more than that in case 2
No. of shapes in case 4 is 9 + 4 = 1 3 more than that in case 3.
No. of shapes in case 5 is 1 3 + 4 = 1 7 more than that in case 4.
No of shapes in case 6 is 1 7 + 4 = 2 1 more than that in case 5.
Now, no. of shapes in case 6 is 6 6 . So case 7 will have 25 more = 9 1
Then case 8 would have 29 more = 1 2 0
Then case 9 would have 33 more = 1 5 3
Then case 10 (that is the question) would have 37 more = 1 9 0