FILE No.95Unsolved
You want to cut a round cake into as many pieces as possible with three straight cuts of a knife. You do not move the pieces or stack them.
Each cut goes straight down through the cake, from one edge to the other, so seen from above you are drawing three straight lines across a circle. The cuts may be placed anywhere.
One cut makes 2 pieces. Two cuts make at most 4.
What is the largest number of pieces three cuts can make?
If you get stuck, open the hints one at a time, in order.
How many pieces do 2 cuts make at most?
How should the third cut cross the others to add the most?
Into how many segments is the third cut divided?
What is the largest number of pieces three cuts can make?
Choose the answer closest to the truth.
7
The answer is: 7.
Make the third cut cross both of the first two cuts inside the cake. It crosses two lines, so it is split into 3 segments, and each segment splits one piece in two. That adds 3 pieces: 4 + 3 = 7.
If all three cuts pass through the same point, you only get 6.
Cutting through one point, or parallel cuts, gives fewer pieces.
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