This is puzzle asked by many companies may be not exactly same word by word but with slight variations. So the problem description is :
Six pirates must divide $600 among themselves. The following procedure should be followed.
- Senior most pirate will propose way to divide the booty.
- All the pirates will cast a vote against or in favor of the proposal.
- If there is at least half vote in favor of the proposal the proposal will be realized.
- If proposal gets less than half vote, the senior most pirate who proposed it will be thrown in to sea.
All the pirates are highly intelligent and are capable in making the most profitable solution for himself.
How much money each pirate will get?
Solution :
In this whole pirate story one thing is quite clear and that is your life is safe till there exist at least one pirate on the deck who is senior than you.
Lets pirates names with decreasing seniority order are P1,P2, P3, P4, P5,P6 and P1 is the senior most and P6 is the junior most.
Now P6 is the junior most pirate but his life is safe because he will never get chance to propose division plan.
Now consider the situation case 1 when only P5 and P6 left on the ship. This situation is the most favorable for P5 he can propose following division plan
P5 — $600
P6 — $0
P6 will be helpless in this situation P5 can simply cast vote in his favor and keep all the money. P6 will try its best to avoid this situation.
now case 1 is only possible if P4 P5 P6 are left and P4 get thrown in to sea
now in case 2 where P4 P5 P6 left P4 can survive the situation by giving some money to P6 and giving nothing to P5 because P4 knows P6 will get nothing if he dies and thus P6 should be happy whatever he gets so P4 proposed following plan
P4–$599
P5-$0
P6-$1
but you can reach case 2 if you had reached to a situation case 3 when P3 P4 P5 P6 are left on the ship and P3 lost the proposal and thrown in to the sea.
P3 can survive if he gets two votes so apart from securing his own vote he need one more vote. P3 knows P5 will not going to anything if he vote against me because in that case P4 will make the case 2 solution giving $0 to P5. So P5 should be happy whatever he gets instead of nothing and thus P3 Proposes following division plan
P3-$599
P4-$0
P5-$1
P6–$0
but to reach case 3 you have to go through case 4 when P2 P3 P4 P5 P6 was left on board. now P2 need 3 votes so he has to secure at least 2 more
P2 knows P4 will be happy if i provide anything more than 0 because if he votes me out P3 will going to give him nothing so he will be happy in $1 similarly P6 should be happy in $1 because that is the max he can get in any case and in fact if he miss this chance may be P3 will not going to give him anything at all. So P2’s plan is
P2–$598
P3-$0
P4-$1
P5-$0
P6-$1
But before reaching to case 4 you have to reach case 5 when all are alive and on the board P1 P2 P3 P4 P5 P6
now P1 need 2 more votes apart from his vote. P1 knows P3 will be happy in $1 because he is going to get 0 if P2 becomes the senior most. Similarly P5 should be happy in $1 too. So P1 proposed following plan —
P1-$598
P2–$0
P3-$1
P4-$0
P5-$1
P6-$0
so pirate P1 get the maximum amount $598.
important Appeal—
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