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        riddles >> microsoft >> simple question
        
(Message started by: mad on Jul 31^st, 2007, 1:50pm)

Title: simple question
Post by mad on Jul 31^st, 2007, 1:50pm

Given a rectangular (cuboidal for the puritans) cake with a rectangular piece removed (any size or orientation), how would you cut the remainder of the cake into two equal halves with one straight cut of a knife ?

Title: Re: simple question
Post by Paragon on Aug 4^th, 2007, 8:20pm

I can remember another question of this type.
Assuming that the mass is uniformly distributed,the answer was to hang the cuboid with a string ( now all of us know the centre of gravity, from our 7th grade physics course perhaps )
if you extend the line made by the string with which the cuboid is hanged and cut along this line, You can split the cuboid into two equal halfs.

BUT THERE IS A PROBLEM
I dont now how to hang a cake with a string so that it still remains intact ???

and I dont think I am right in saying that the mass should be evenly distributed, It doesnt matter perhaps.....

Title: Re: simple question
Post by JocK on Aug 5^th, 2007, 5:59am

on 07/31/07 at 13:50:00, mad wrote:

Piece of cake! ;) If the removal of the piece [hide]left the edges of the cake unaffected, I'd simply slice the cake in the normal way[/hide]...

Title: Re: simple question
Post by mikedagr8 on Aug 10^th, 2007, 5:02am

assuming mass is evenly distributed, we can cut the cake in half no matter what. pex has diagrams to show this if he comes along ::) (I hope i am correct), but i can do it visually, unless someone can show me a case where i cant.

Title: Re: simple question
Post by Grimbal on Aug 10^th, 2007, 5:30am

I think the expected answer is:
Cut along the line that goes through the center of the cake and the center of the hole. Both halves are exactly half the original cake minus half the hole. This works with any cake and any hole that has central symetry, assuming the hole doesn't overlap outside of the cake.

Title: Re: simple question
Post by cchris on Aug 21^st, 2007, 5:10pm

That, or [hide]just cut it into the top and bottom layer[/hide]. No one said the cake had frosting.