Solution to Puzzle 4

[kunal naidu]

Hi all,

Here is the solution to puzzle 4

Q. There are 5 people and 100 gold coins. They need to share it among themselves. They decide the following scheme to share the coins:
The oldest among them will propose a division scheme. Then all of them, including the oldest who proposed the scheme will vote. If 50% or more agree to it then, that scheme is followed, else the oldest is killed, and the entire procedure is repeated again. Considering all the 5 are smart, greedy and do not want to die, what is the scheme that the oldest in the group should propose

A: The oldest person will propose a 98 : 0 : 1 : 0 : 1 split, in other words the oldest  gets 98 coins, the middle gets 1 coin and the youngest gets 1 coin.

 Let us name the people (from oldest to youngest): Alex, Billy, Colin, Duncan and Eddie.

Working backwards:

 2 People: Duncan splits the coins 100 : 0 (giving himself all the gold). His vote (50%) is enough to ensure the deal.

3 People : Colin splits the coins 99 : 0 : 1. Eddie will accept this deal (getting just 1 coin), because he knows that if he rejects the deal there will be only two pirates left, and he gets nothing.

4 People : Billy splits the coins 99 : 0 : 0 : 1. By the same reasoning as before, Eddie will support this deal.

5 People : Alex splits the coins 98 : 0 : 1 : 0 : 1. By offering a gold coin to Colin (who would otherwise get nothing) he is assured of a deal.

Pretty interesting....i think...although many of you have mailed me the answer as 34, 33,33...and so on.....now u know, how far u were from the actual answer.....so always give the puzzles a good thought, if it was straightforward, I would not post it, and neither will any interviewer ask it.

Regards

Kunal Naidu

[ARPIT PAREEK]

@kunal your logic for 2 and 3 person is okay..
but for 4 person... there is a chance that eddie (youngest one) decline the deal.. as even after declining the deal he can get 1 coin... so i think for the case with 4 people.. oldest one should suggest... 98:0:2
so now if the answer for 4 people is changed that will also affect the answer for 5 people as in given answer (5 people case) eddie is getting 1 coin where in 4 people case he may get 2 coins...so he will reject the given proposal... please correct me if i m wrong...


--
Regards,
Arpit Pareek,
Third Year Undergraduate,
Department Of Mechanical Engineering,
IIT Bombay.

Email : pareek...@gmail.com //  arpitp...@iitb.ac.in
Pnone : +91-8268934689

[Anvay Upadhye]

For the four people case, I think it should be 99:0:1:0, Duncan has to
accept because if he rejects he will get 0 according to the 3 person
case.From this the 5 person case follows logically, as 98:0:1:0:1, as
mentioned. Both Collin and Eddie have to accept otherwise they get 0.

[ARPIT PAREEK]

yes this solution looks right... :)