[Haskell-cafe] Health effects

[ajb at spamcop.net]

G'day all.

Quoting Adrian Neumann <aneumann at inf.fu-berlin.de>:

> I often wonder how many cuts you need to divide a steak in n pieces.

One, if the cut is allowed to be curved and self-intersecting.

I think that the spirit of the problem, though is encapsulated in this
question: Given a circle, what is the maximum number of pieces that you
can divide it into by performing n straight cuts?

This is a great problem to set undergraduates, because if you work out
some small values of n on paper, you get:

     n   #pieces
     0   1
     1   2
     2   4
     3   7

Most undergrads will stall at this point trying to work out how to
place the third line to get 8 pieces, and probably come up with an
incorrect justification for why it should be 2^n.

The details are here:

     http://www.research.att.com/~njas/sequences/A000124

Cheers,
Andrew Bromage