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        riddles >> easy >> The Circle and Lines
        
(Message started by: TenaliRaman on Jul 23^rd, 2004, 7:18am)

Title: The Circle and Lines
Post by TenaliRaman on Jul 23^rd, 2004, 7:18am

You are given 21 lines and a circle. What is the maximum number of parts that you can divide the circle with the help of the 21 lines?

Title: Re: The Circle and Lines
Post by Grimbal on Jul 23^rd, 2004, 1:30pm

Is que question equivalent to: in how many pieces can you cut a round pizza with 21 straight cuts?

It should be ::[hide]1+21*(21+1)/2 = 232[/hide]:: then

Title: Re: The Circle and Lines
Post by tseuG on Jul 23^rd, 2004, 1:33pm

[hide]Proceeding from one line segment seems to simplify things[/hide].

Title: Re: The Circle and Lines
Post by TenaliRaman on Jul 24^th, 2004, 11:51pm

Bravo Grimbal and TseuG!
:)

Title: Re: The Circle and Lines
Post by Noke Lieu on Jul 25^th, 2004, 11:53pm

for our irregulars:
In case discombobulated by Grimbal's equation, try:
[hide]
(x[sup2]+x+2)/2
[/hide]
Its the same thing, I just find it nice when people put brackets in places where I expect them.... :P

and its hidden for postderity. In 6 months, when new folk turn up, it isn't in their face straight away, only being an early post.

Title: Re: The Circle and Lines
Post by Speaker on Jul 26^th, 2004, 1:56am

So, what sort of shape are those pizza pieces? They are not wedge slices are they. So, are they squares? Does anybody have a picture?

Title: Re: The Circle and Lines
Post by towr on Jul 26^th, 2004, 2:18am

they're not all the same sort of shape.. Some include a part of the edge of the pizza which is a curve, other piece are bounded solely by straight lines, some by three, some by four.

Title: Re: The Circle and Lines
Post by towr on Jul 26^th, 2004, 3:43am

Here's one way of dividing the circle/pizza..

It does mean some people get an awfully small piece though, and one person get's a disproportionately large piece (feel free to determine how much)..

Title: Re: The Circle and Lines
Post by Speaker on Jul 26^th, 2004, 4:53pm

Thanks towr
That is a great image. The rule I learned is that the guy who cuts the pizza (or cake or whatever) had to choose last. That made the cutter be carefule to keep all the pieces the same size. :D

Title: Re: The Circle and Lines
Post by Grimbal on Jul 27^th, 2004, 5:41am

If you are last to chose, you better make a mess with the cake and make a lot of crumbs. Since you are last to take your piece, you can have all the crumbs.
;D

I am from a large family. I know this by experience.