There are 5 pirates who have found 100 gold coins. The pirates are ranked by seniority from Pirate 1 (the most senior) to Pirate 5 (the least senior). The pirates must decide how to distribute the coins, but there are specific rules:
- The most senior pirate (Pirate 1) proposes how to divide the coins.
- All the pirates, including Pirate 1, will then vote on the proposal. If 50% or more agree, the proposal is accepted and the coins are divided accordingly.
- If less than 50% agree, Pirate 1 is thrown overboard, and the next most senior pirate (Pirate 2) makes a new proposal.
- Pirates are ruthless and logical: they want to get as many coins as possible and would rather see another pirate thrown overboard than receive fewer coins.
Objective:
Pirate 1 must come up with a proposal that will be accepted by the majority to keep themselves alive and still get as many coins as possible.
Solution
To solve this puzzle, we need to understand how each pirate will act based on their goal to maximize their own share of the gold. Pirates will also consider survival, meaning they will only support a proposal if it gives them more than they would get in a future proposal or if it keeps them alive.
Step-by-Step Solution for 5 Pirates and 100 Gold Coins Puzzle:
Let’s start with the simplest scenario and work backward, thinking about what each pirate would do if only a few were left.
Step 1: If Only Pirate 5 is Left
If all the other pirates have been thrown overboard and only Pirate 5 remains, Pirate 5 would keep all 100 coins. There is no one to vote against them, so Pirate 5 will take everything.
Step 2: If Pirates 4 and 5 are Left
Pirate 4 knows that if they are thrown overboard, Pirate 5 will keep all 100 coins. Therefore, Pirate 4 will propose a distribution where Pirate 5 gets 0 coins, and Pirate 4 will keep all 100 coins. Pirate 5 would vote against this if they could, but with only two pirates, Pirate 4’s vote is enough to pass the proposal.
Step 3: If Pirates 3, 4, and 5 are Left
Pirate 3 knows that Pirate 4 would keep all 100 coins if Pirate 3 is thrown overboard. To prevent this, Pirate 3 can offer Pirate 5 1 coin (since Pirate 5 gets nothing in Pirate 4’s proposal). Pirate 4, meanwhile, would receive 0 coins in Pirate 3’s plan. Pirate 3 will keep the remaining 99 coins.
Pirate 5 would vote for this because 1 coin is better than none, so Pirate 3’s proposal passes.
Step 4: If Pirates 2, 3, 4, and 5 are Left
Pirate 2 needs to secure at least two votes, including their own. Pirate 2 knows that Pirate 3 will give Pirate 5 one coin. So, Pirate 2 can offer Pirate 4 1 coin (since Pirate 4 gets nothing in Pirate 3’s proposal). Pirate 5 would still get 1 coin, and Pirate 2 keeps 98 coins.
Both Pirate 4 and Pirate 5 would vote for this plan, because they are getting the same or better than they would under Pirate 3’s proposal. Therefore, Pirate 2’s proposal is accepted.
Step 5: If All Five Pirates Are Left
Pirate 1 knows they need to get two additional votes to avoid being thrown overboard. Looking at the previous cases:
- Pirate 3 receives nothing in Pirate 2’s plan, so Pirate 1 can offer Pirate 3 1 coin.
- Pirate 5 only receives 1 coin in Pirate 2’s plan, so Pirate 1 can offer Pirate 5 2 coins.
Pirate 1 will keep 97 coins. Pirates 3 and 5 would vote for this proposal, because they are getting better deals than they would from Pirate 2’s proposal.
Final Distribution
Pirate 1 proposes the following distribution:
- Pirate 1: 97 coins
- Pirate 3: 1 coin
- Pirate 5: 2 coins
- Pirate 2: 0 coins
- Pirate 4: 0 coins
Pirate 3 and Pirate 5 will vote in favor of this, so Pirate 1’s proposal passes.
