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 Does it continue? 1: Chord regions (Posted on 2017-09-13)
In his paper The Strong Law of Small Numbers Richard Guy states "There aren't enough small numbers to meet the demands made of them."

It's a great list of 35 examples where the pattern noted early on may or may not continue. Unfortunately, if you read it, you will give away a series of around 10 puzzles I plan to create from it.

Before trying the problem "note your opinion as to whether the observed pattern is known to continue, known not to continue, or not known at all."

Place n points around a circle so that no three of the C(n,2) chords joining them are concurrent. Count the number of regions into which the chords partition the circle.

n=0, 1 region
n=1, 2 regions (a single chord)
n=2, 4 regions (the chords form a triangle)
n=3, 8 regions
n=4, 16 regions

A pattern has emerged. Does it continue?

 No Solution Yet Submitted by Jer No Rating

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 Does it continue? | Comment 7 of 9 |
I know it's our habit to only share a solution or possible solution here on perplexus.  With this "Does it continue?" series, feel free to share whether you guessed correctly or not.

I had seen this one before so didn't have to guess.

chun's answer is the minimum correct response, but how about a general formula?  I recall deriving it years ago at a weeklong conference on problem solving.

 Posted by Jer on 2017-09-17 21:10:32

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