Pirate Logic Question
A group of 5 pirates obtained 100 gold coins. They are deciding how many coins to give to each person by voting. Here is how the vote works:
- The first pirate suggests a way to split the coins. All pirate including the first pirate is allowed to vote. They vote by saying yes or no. If the amount of people saying no outnumber the amount of people saying yes, the first pirate gets killed.
- After the first pirate gets killed, everyone votes for the second pirate's plan. Each time a pirate gets killed it passes on to the next pirate.
- If the amount of people saying yes is the same , or greater than the amount of people saying no, that plan will be applied to the pirates.
The main goal of the pirates is to survive. The secondary goal of the pirates is to maximize the number of coins gained. Every pirate is very logical and they know all other pirates are logical. If you are the first pirate, what is the most amount of coins you can get without dying?
The answer is 98.
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1 solution
If you start by thinking about the first pirate, it is hard to make a progress. However, it will be much easier to start with the situation where only 2 pirates are alive.
In this case, the fourth pirate can give all the coins to himself. When there is only 2 people, it is impossible for the amount of "no" to outnumber the amount of "yes", since the fourth pirate can vote for his own plan. Therefore, the fifth pirate want to avoid this situation.
Let's think one step back. When there is 3 pirates left, the third pirate need someone to agree with him in order to survive. Well, giving 1 coin to the fifth pirate will work. This is because if the third pirate gets killed, the fifth pirate will not get any coins. Also, keep in mind that giving any amount of coins to the fourth pirate won't work because if the third pirate gets killed, the fourth pirate can get all the coins.
When there is 4 pirates left, the second pirate still require 1 person to agree with him. When the second pirate gets killed, the fourth pirate will get 0 coins as figured in the last step. So, giving the fourth pirate 1 coin will be enough. Giving coins to any other pirate will not work.
Back to the first situation when there is 5 pirates, the first pirate need 2 people to agree with him to not be outnumbered. Giving 1 coin to the third and fifth pirate will be a perfect solution. Because when the second pirate is making the plan, the third and fifth pirate will get nothing. That leaves 98 coins for the first pirate.
This is the kind of problem that you need to work backwards. It is also important to identify what will happen if you give money to a certain pirate.