p=frac{n^2+n+2}{2}
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Day 277: A Lazy Caterer

The lazy caterer’s sequence is used to work out the maximum number of pieces of a pancake or pizza (anything circular) that can be made with a given number of straight cuts.

3 cuts can create 6 pieces if all cuts meet at a single point, but 7 if they don’t.

It isn’t actually called the lazy caterer’s sequence at all – it is really the central polygonal number sequence. In three dimensions, it is known as the cake number.

Its formula is:

p=frac{n^2+n+2}{2}

p is the number of pieces, n is the number of cuts used.

Sticking 23 in the equation provides:

p=frac{23^2+23+2}{2}=frac{529+23+2}{2}=frac{554}{2}=277

That then, is why I’m writing about it today.

 

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  1. Day 287: The Day This Blog Became Useful | ThomasJPitts' Blog
    14th October 2013 @ 10:20 pm

    […] about a quiz on BBC Four. Some people call it Only Connect. Because that’s its name. A few days ago I posted about the Lazy Caterer’s Sequence and this was the answer to a question on the quiz. […]

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