## Solution to Puzzle #169: Division of a Cake

This puzzle was not as easy as it looked…many people sent solution, but only Suman Saraf and his daughter Mahi sent the correct ones.

To copy a line I really liked from Suman’s solution – The essence of fair or envy free devision is that the only reasons a person could be unhappy are if they themselves made a bad choice or a bad cut. Nothing else should give them a reason to be unhappy.

Here is a simple way of doing it for any number of people (say n), people are named as X(1), X(2), …., (Xn).

Assume they are all sitting in a circle. X(1) makes a cut that he/she thinks is 1/n of the overall cake. The one who made the cut has the “current marker”.

X(2) has the following choice – If (s)he thinks that the cut is unfair, i.e. more than 1/n, then (s)he can trim it further until (s)he thinks it is 1/n, or just let it pass. Therefore, the piece will either reduce in size, or remain what it was. If X(2) trims it, then (s)he gets the “current marker”, if not, the marker remains with X(1). We continue this way until we reach a point where the turn comes back to the person with the “current marker”, at which point, they take the piece they had cut/ trimmed. It is “fair” for them to take it as they cut it themselves, and everyone else in the circle had the opportunity to take it and they chose not to.

After one person it out, we repeat the process for (n-1) people.

Please do think about it, and may be even try it at home, I am sure a lot of cake eating will happen 🙂

Hope you all enjoyed the puzzle!

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### 1 Response to Solution to Puzzle #169: Division of a Cake

1. This is awesome. Thanks a ton.