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Puzzles

Cake Cutting

Puzzle

Mary baked a rectangular cake. Merlin secretly carved out a small rectangular piece, ate it and vanished! The remaining cake has to be split evenly between Mary's two kids. How could this be done with only one cut through the cake?

Source

Heard a long time ago, in 1990s.

Solution

(by Yuri Robbers): There are two solutions to this problem. The first solution is perhaps a little bit silly, and it only works if the cake is vertically symmetrical. In that case it owuld be possible to halve the cake horizontally. The top half and the bottom half would then be identical.

A less silly solution is to cut along the line that runs through the center of the original cake, and through the center of the piece that is missing. If the centers happen to coincide, then any line through that joint center will do. Any rectangle is halved by any line through its center. Cutting through the center of the cake therefore halves the cake, while cutting through the center of the missing piece, halves the missing piece.

Previous Puzzle: Rope Escape

Rajeev is trapped atop a building 200m high. He has with him a rope 150m long. There is a hook at the top where he stands. Looking down, he notices that midway between him and the ground, at a height of 100m, there is a ledge with another hook. In his pocket lies a Swiss knife. Hmm... how might he be able to come down using the rope, the two hooks and the Swiss knife?

Next Puzzle: Fox in a Hole

Consider five holes in a line. One of them is occupied by a fox. Each night, the fox moves to a neighboring hole, either to the left or to the right. Each morning, you get to inspect a hole of your choice. What strategy would ensure that the fox is eventually caught?

8 Dec 2008
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