- #1

- 14

- 0

## Main Question or Discussion Point

Warning: I do not know the answer to this one. If this will keep you up at night, do not read on. I was asked this in a job interview a long time ago. They did like my answers, even though they were "wrong".

Still here? OK.

You are presented with a rectangular cake.

Somewhere at an arbitrary location in this rectangular cake, an arbitrarily sized rectangle of cake is missing.

The missing rectangle does not touch the edge, though it may be very close to it. In other words, the cake is not missing a corner.

Using two separate cuts, divide the cake into two equal (volume) pieces.

Wrong solution #1 (hidden text):

Using one cut, slice the cake horizontally, the top half is the same volume as the bottom half.

Wrong solution #2 (hidden text):

Use two knives. Balance the cake on one knife, then cut once along the line of balance using the second knife. Each half has the same volume. Note that there are an infinite number of solutions with this method

What are your thoughts? Every two-cut method I come up with has a case that does not work.

Still here? OK.

You are presented with a rectangular cake.

Somewhere at an arbitrary location in this rectangular cake, an arbitrarily sized rectangle of cake is missing.

The missing rectangle does not touch the edge, though it may be very close to it. In other words, the cake is not missing a corner.

Using two separate cuts, divide the cake into two equal (volume) pieces.

Wrong solution #1 (hidden text):

Using one cut, slice the cake horizontally, the top half is the same volume as the bottom half.

Wrong solution #2 (hidden text):

Use two knives. Balance the cake on one knife, then cut once along the line of balance using the second knife. Each half has the same volume. Note that there are an infinite number of solutions with this method

What are your thoughts? Every two-cut method I come up with has a case that does not work.