How do I set up difference equations for intersecting ovals?

[morry]

Ok, I am not sure if this is the right section, but seeing that difference equations are the discrete version...

Now the question is :
Into how many regions do n simple ovals divide the plane, given that every oval meets every other oval in two points and no point in the plane is common to more than two ovals.

I have NO idea how to go about this. Anyone care to shed some light?

 

[morry]

Any ideas at all? Is this the right section?

 

[Zurtex]

Are you sure this is the full question and doesn't have any other parts? What sort of work have you been doing recently on this topic? I'm just trying to get some context because the question doesn't seem very full.

 

[HallsofIvy]

Looks to me like an induction question. Two ovals, meeting in two points, divide the plane into 4 regions. 3 ovals, each meeting each other in two points, divide the plane into 9 regions. Hmm, should we guess n²? I suspect you can find a difference equation relating the value for n ovals with the value for n+1 ovals.

 

[morry]

Thanks for the replies guys. :D

Halls, what would be some of the steps involved in setting up these types of equations? We have covered how to solve them, but not how to set them up. Which is what I am having trouble with.