JOMO 7, Short 3
Probability
Level
3
What is the maximum number of regions in which lines divide a plane into?
The answer is 29.
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
by recurrence we see that if no three lines are concurrent(to get max no of regions) a(n)=a(n-1)+n [a(p)=no. of regions into which plane is divided by pth line] a(1)=2 solving it we get a(n)=[n(n+1)/2]+1 {the sq bracket is not the box function}