25 June 2017

A very interesting puzzle

I understand the problem is attributed to Pythagoras. (I am not sure of the veracity of the story). In any case, my friend Prodipto posted this in our school Whatsapp group. Try it…

In a party that had 100 guests, the first guest was given 1% of a large cake. The next guest got 2% of what was left. And the next got 3% of what was left…. on and on… the 99th guest got 99% whatever was left at that time and the 100th guest got the final (100% of) leftover.

Which guest got the largest piece?

…..

Adding the answer here…

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Posted June 25, 2017 by Rajib Roy in category "Puzzles

12 COMMENTS :

  1. By Marek Cyzio on

    The equation of N’th person share is f(n) = 1/100 * n * (1-sum on i from 1 to n-1 of f(i)). The next step is to take a derivative of this function and find zero but it’s Sunday night so I will pass.

    Reply
  2. By Anjan Das on

    nice puzzle! my sympathies to the last 50 odd guests; all they get are some molecules, atoms and sub-atomic particles of the cake 🙁

    Reply
  3. By Rajib Roy on

    Now for the answer – it is the 10th person. A few people used Excel. Some more sent the answer but did not state how they arrived at the answer. Narayan had the full solution including how he arrived at the answer. The following also concluded the answer has to be the 10th person – Harmindar, Pradeep, Raghu, Gowri, Ramesh an Prodipto himself. Here is my proof…

    Reply

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