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 simple question   « on: Jul 31st, 2007, 1:50pm » Quote Modify

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 ?
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Paragon
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 Re: simple question   « Reply #1 on: Aug 4th, 2007, 8:20pm » Quote Modify

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.....
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JocK
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 Re: simple question   « Reply #2 on: Aug 5th, 2007, 5:59am » Quote Modify

on Jul 31st, 2007, 1:50pm, mad wrote:
 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 ?

Piece of cake! If the removal of the piece left the edges of the cake unaffected, I'd simply slice the cake in the normal way...
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solving abstract problems is like sex: it may occasionally have some practical use, but that is not why we do it.

xy - y = x5 - y4 - y3 = 20; x>0, y>0.
mikedagr8
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 Re: simple question   « Reply #3 on: Aug 10th, 2007, 5:02am » Quote Modify

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.
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Grimbal
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 Re: simple question   « Reply #4 on: Aug 10th, 2007, 5:30am » Quote Modify

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.
 « Last Edit: Aug 10th, 2007, 5:31am by Grimbal » IP Logged
cchris
Senior Riddler

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 Re: simple question   « Reply #5 on: Aug 21st, 2007, 5:10pm » Quote Modify

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