Brain Teasers
Cutting the Cake
During her birthday party, Mary noticed that from a rectangular cake a rectangular piece was missing (it doesn't matter where). With two guests remaining without cake, she wanted to give them equal pieces of the cake. Remembering Professor Voronka's geometry class, she said, "I know how to cut the cake in half using a single cut!" and proceeds to do so.
How did she cut the cake using a SINGLE STRAIGHT cut? Can you think of another way?
Assume that the cake is uniform so that both pieces will have the same ingredients no matter how the cake is cut.
How did she cut the cake using a SINGLE STRAIGHT cut? Can you think of another way?
Assume that the cake is uniform so that both pieces will have the same ingredients no matter how the cake is cut.
Hint
To the first way:This wouldn't be possible if the cake was two-dimensional.
To the second way:
What are the ways you can divide a rectangle in half using a straight line? (There are more than 4)
Major Hint:
Where do these lines all cross?
Answer
First Way:Cut the cake horizontally in the middle.
Second Way:
Cut the cake along the centers of the two rectangles. (i.e., the missing piece and the entire cake)
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Comments
Nice teaser!
May 14, 2003
Please can you explain the second method a little better? I don't understand what you mean.
May 22, 2003
Anyone? Feel free to enlighten me.
Didn't quite get that one.........
That was a brilliant teaser. To Anonymous: Any line that passes through the centre of a rectangle cuts it into two equal halves. So, if you drew a line that passes through the centre of the whole cake and the centre of the missing part, it would divide both rectangles into two equal halves. So both remaining parts will have exactly half of the cake - exactly half of the hole. Hence the cake has been divided into two equal halves.
First, Krishnan, you used "hole" instead of "whole". Secondly, I think that the rectangle's position should probably be specified, to make it more understandable.
Easy teaser, but nice!
Pissfer, it made it easier to NOT specify the location of the second rectangle since that forces you to consider only generalized solutions.
Pissfer, it made it easier to NOT specify the location of the second rectangle since that forces you to consider only generalized solutions.
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