Another nice question
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)
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
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