### 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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