how do you split a circle into 8 pieces with only 3 lines?

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Request for Question Clarification by pafalafa-ga on 08 Oct 2003 15:43 PDT

Are you sure the question is meant to ask about cutting a circle?

This question is a well-known "thinking outside the box" type of
challenge, except it's usually asked about cutting a round cheese,
which, being three-dimensional, can be cut into 8 pieces with three
lines.  But a circle...?  I don't think so, not if the lines have to
be straight.

must they be straight lines only?

If the lines are constrained to be straight then it can't be done. 

The formula for the number of regions when the interior of a circle 
is divided by n lines is:

f(n) = n(n+1)/2  + 1

So, for n = 3, f(n) = 7. 

For an explanation of the derivation of this formula see:

http://mathforum.org/library/drmath/view/55262.html


Cheers,

Eadfrith



is giv

the version that i heard of this riddle goes something like: how do
you cut a round cake into 8 pieces with 3 vertical straight-line cuts
(vertical, so you can't use the three-dimensionality of the cake...)

this is still in the "thinking outside the box" spirit. here's the
solution (i left a space so that if you still want to think about it,
you won't be forced to read it immediately:


























































































make two orthogonal cuts in the cake, cutting it into 4 pieces.

move the 4 pieces to line them up together.

make another cut, cutting each of the pieces into two pieces . . .

cheers,
dannidin