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Friday Puzzler -- Cutting cake

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Friday Puzzler -- Cutting cake

#1

Friday Puzzler -- Cutting cake

Alex Y

My wife and I baked a nice rectangular sheet cake, and iced it in the pan with fudge icing. I cut out a rectangular piece of the cake for my wife and me to keep, and told our two kids they could have the rest for their families if they could cut the remaining cake exactly in half with one straight-line cut. Because the cake was iced, neither wanted to make a horizontal cut, possibly leaving all the icing to his or her sibling's family.

How can they achieve the desired cut?

P.S., if your solution depends on my taking the rectangular piece out of a particular location, assume I took it from somewhere else ;-)

Re: Friday Puzzler -- Cutting cake

#2

Re: Friday Puzzler -- Cutting cake

John Veerkamp

trapizoidal cut

Re: Friday Puzzler -- Cutting cake

#3

Re: Friday Puzzler -- Cutting cake

Alex Y

Needs to be one straight-line cut. And I'm not sure what trapezoidal cut will work anyway if this is what the cake looks like after I've taken my rectangular piece.


The desired method of determining the straight-line cut works for even weird cases like this.

Re: Friday Puzzler -- Cutting cake

#4

Re: Friday Puzzler -- Cutting cake

Henry Higginbotham

Slice through the centroids?

Re: Friday Puzzler -- Cutting cake

#5

That was quick!

Alex Y

Yes, any two-dimensional shape that is symmetrical on two axes is divided in half by any line through its center. So the line through the centers of both the original cake and the hole I left in the cake will divide both the cake and the hole into two equal pieces.

Nice job.

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