### Brain Teasers

# Birthday Cake

Suppose you are given a birthday cake which is round in shape (like a perfect circle) and you are asked to make eight equal pieces out of it by using a knife only three times. How would you proceed?

### Answer

Use the knife a first time to cut it across one of its diameters. Then use the knife a second time to cut across another diameter and you will have four equal parts. Use the knife a third time to cut the cake horizontally, half way across its thickness, and you have the eight equal pieces!!!Hide Answer Show Answer

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## Comments

Although they are the same size, they aren`t really equal because 4 are from the top and 4 are from the bottom. You could cut the cake twice as the answer states, but then move the pieces so they are all in a line and make one final long cut splitting all 4 pieces into 8 completely equal pieces. eh?

You know, I exhaust most teaser books i know of, go searching for new ones, and run into ones i've already seen.

Half of the little kids would be ticked to not get any icing as well! And if you saw this one before, Mogmatt, you could have submitted it first and not have had to complain.

For the 3rd cut, you could also put the quarter pieces on top of each other and cut straight down.

this shud b in trick not maths

this shud b in trick not maths

I agree with canu. Then all the little kids would get icving too.

I don't think a piece of cake is worth that. Who would limit you to only 3 cuts?

Cute, but then the peices are smaller. I call a bottom piece!

I don't understand the way that the answer is worded at all -- did they mean that after the first two cuts are made the pieces are stacked on top of each other or in a line and **then** the final cut is made? Because otherwise, if the four pieces are left as they are, it is impossible to just make one more cut and end up with eight equal pieces.

???

???

My solution was to cut an inner circle with a radius of 1/sqrt(2) times the cake radius and then cut two diagonals. At least everyone gets some of the top icing that way.

To heck with the problems, I just Love Java's solutions - Way to go!

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