Five pirates having 100 gold coins in a ship – puzzle (Logical question)

Logical Question/ Puzzle: Five pirates & 100 gold coins in a ship

• Five pirates say P1 to P5  (youngest to oldest) travelling in a ship & have a bag containing 100 gold coins.
• Pirates decided to distributes the coins, among themselves.
• Oldest pirate P5 proposes a plan to distribute the gold coins.
  • All pirates including oldest one, can either vote in favor or against the plan.
• If 50% or more pirates voted in favor of plan, then coins will be distributed as per the plan.
• Else, pirate proposing the plan will be thrown from a ship.
• The next senior most pirate say P4 will proposes the new plan.
• The process keep on moving to next pirate until proposal is accepted.
• The oldest pirate wants to stay alive and would like to keep maximum coins.
• What plan P5 will proposes, so that he get 50% or more votes, in his favor?

Solution: five pirates & 100 gold coins in a ship (logical question/puzzle)

All pirates will try to maximize their profit. We will evaluate the thought process of  youngest pirates P1 and P2 and similar process will be applied to other pirates. We will finally look into the pirate P5′ s prospective.

1. If P1 and P2 would like to distribute coin between them and P2 proposes a plan.
   • P2 constitute 50% of vote share.
     • P2 come up with a plan to keep 100 coins and 0 coins for P1.
   • P2 will stay alive and kept maximum coins.
   • The result is P2 = 100 and P1 = 0.
2. If P1, P2 and P3 would like distribute coin among themselves.
   • P3 being the senior most pirates, will propose a plan.
   • P1 pirates knows if P3 proposal not get accepted then P2 will take over.
     • P1 would not get anything (Point 1)
     • P1 would vote for P3 if P3 can share something with P1.
   • P3 knows that if his proposal not get accepted then P2 will get 100 coins.
     • P3 will offer 1 gold coin to P1 (as P1 would not get any thing if P2 take over).
     • P1 will vote for P3 if P1 gets 1 coin.
   • P3 propose to distribute coins as P3 =99, P2 = 0 and P1 = 1.
     • P1 will vote for proposal and P3 will get more than 50% of vote (including his vote).
3. If P1, P2, P3 and P4 would like distribute coin among themselves.
   • P4 being the senior most pirates, will propose a plan.
   • P4 Knows if his proposal not get accepted then P3 will take over.
     • P3 will get 99 coins and P2 will get nothing   (Point 2)
     • P4 will try to earn the vote of P2 and P4 will offer 1 gold coin to P2.
   • P2 knows if P4 proposal does not get accepted then P3 would give nothing (to P2).
     • P2 accepts 1 gold coin from P4.
   • P4 proposes a plan to distribute coins as P4 = 99, P3 = 0, P2 = 1 and P1 = 0.
     • P2 will vote in favor of P4 and hence P4 will get 50% of votes.
4. P1, P2, P3, P4 and P5 would like distribute coin among themselves and P5 will propose a plan.
   • P1 and P3 knows if P5 proposal does not get accepted then P4 will take over.
     • P4 would give nothing to P1 and P3  (Point 3)
     • If P1 and P3 get something from P5,then they will vote for P5.
   • P5 knows that if his proposal does not get accepted then
     • P4 will get 99 coins & P4 will give nothing to P1 and P3.
     • P5 needs couple of vote to cross 50% vote share.
     • P5 offer 1 coin each to P1 and P3 and they will accept P5’s proposal.
   • P5 proposes a plan to distribute coins as P5 = 98, P4 = 0, P3 = 1, P2 = 0 and P1 = 1.
     • P1, P3 will vote for P5 and P5 will more than 50% of votes.