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100 Gold Coins
Five pirates have obtained 100 gold coins and have to divide
up the loot. The pirates are all extremely intelligent,
treacherous and selfish (especially the captain).
The captain always proposes a distribution of the loot. All
pirates vote on the proposal, and if half the crew or more
go "Aye", the loot is divided as proposed, as no pirate
would be willing to take on the captain without superior
force on their side.
If the captain fails to obtain support of at least half his
crew (which includes himself), he faces a mutiny, and all
pirates will turn against him and make him walk the plank.
The pirates start over again with the next senior pirate as
captain.
What is the maximum number of coins the captain can keep
without risking his life?
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Answer Posted / guest
We number the pirate from 1 to 5 (5 is the captain and the
senior level is going down to 1). We will solve problem
from bottom to top.
Let's start the game from 2 pirates => the captain will
take all because he will vote for himself, it means 50% go
"Aye". For sure, the second pirates don't want this
situation because he get nothing. He won't let this
situation happen and he have to choice something when the
team have 3 members.
If the team includes 3, the captain can't get all like
previous situation because he will be killed. He will get
99 coins and the rest for pirate number 1. Number 1 have to
go "Aye" because he don't want the previous case happen.
2/3 accept so the loot will be divided. The number 2 pirate
don't want this case because he get nothing.
If the team include 4, just solve as previous and the
number 4 pirate will take 99 coins, 1 coin for number 2,
number 1 and number 3 get nothing. Number 2 will accept
because he doesn't want the previous case happen. Number 1
and number 3 don't accept but it's not a problem because
number 4 and 2 are accept.
Now come back to our main problem (5 pirates), number 5
need to have at less 3 votes if he doesn't want to die.
Same solution as previous case, Number 5 just get 98 coins,
1 for number 1, 1 for number 3. Number 2 and number 4 get
nothing.
=> Ans: The captain get 98 coins, number 1 and number 3:
each get 1 coin, number 2 and 4 get nothing.
| Is This Answer Correct ? | 22 Yes | 4 No |
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