Solution to Riddle of the Week

Solution to Riddle of the Week: The Pirates and Their Booty

Difficulty level: Hard

By Jay Bennett

An initial assumption that many people make is that Pirate A will need to give himself fewer coins to avoid being voted off and tossed overboard so the others can split the money between fewer people. However, because the greedy pirates don't trust each other to make any deals beyond the set rules, Pirate A can actually take the lion's share of the coins and leave the others with hardly any at all.

SOLUTION

Pirate A should give 1 coin to Pirate C, 1 coin to Pirate E, and keep 98 coins for himself. If he does, Pirates C and E will vote along with him because they know they both will end up with nothing if they don't. The coins will be distributed like this: A:98, B:0, C:1, D:0, E:1.

Let's work through this backwards. Imagine that the only two pirates left are Pirate D and Pirate E. Pirate D will keep all 100 coins for himself because his vote will give him the 50 percent he needs. Distribution: D: 100, E:0.

Now let's imagine that Pirates C, D and E are divvying up the coins. Pirate C will give 1 coin to Pirate E and none to Pirate D. Pirate E will vote along with Pirate C because he knows if they toss C overboard, D will give him nothing. Distribution: C:99, D:0, E:1.

With four pirates, Pirate B will give 1 coin to Pirate D, and Pirate D will vote along with him because he knows that if they throw B overboard, C will give him nothing. Pirate B and D together give the proposal the 50 percent vote it needs to pass. You might think that Pirate B could give 1 coin to Pirate E instead because E knows he cannot get any more coins, but Pirate E will vote to toss B overboard just for the fun of it if he knows his coins will be the same from Pirate C. Distribution: B:99, C:0, D:1, E:0.

Because he knows all this, Pirate A can safely offer Pirate C just 1 coin and Pirate E the same. If the two pirates vote to toss him overboard, they both will be left with nothing when B distributes the coins. Pirate A cannot, for example, give a coin to D instead of C because D would rather throw him overboard and get his one coin from B. Final distribution: A:98, B:0, C:1, D:0, E:1.

What happens to Pirate A after they divvy up the coins is anyone's guess.