Bonus: Logic Puzzles

Here are some logic puzzles to get your brain in game theory mode.

The Pirates’ Booty

Five pirates have just plundered 100 gold coins of treasure. Their ranks, from most senior to least senior are: Captain (C), First Mate (F), Quartermaster (Q), Boatswain (B), and Deckhand (D).

The captain has to propose a distribution of the gold–how much gold each pirate, including himself, gets. All the pirates, including the captain, then vote to accept or reject the proposal.

  • If at least half accept, the proposal is accepted and the gold is split according to the proposed distribution.
  • If less than half accept, the proposal is rejected and the captain is thrown overboard. The next most senior pirate will then make a proposal according to the same rules.

Assume that the pirates’ objective is to maximize their own gold, without getting thrown overboard. If they’re ever indifferent between two situations, they’d rather see someone get thrown overboard than not.

How will the captain make the initial proposal?

Chinese Dumplings

Two Chinese business associates, Ang and Bai, are having dinner and sharing a plate of dumplings.

The two businessmen take turns taking dumplings from the plate.

The Chinese have a very particular culture about dinner table etiquette. Their goal is to maximize the number of dumplings they get, without being rude.

  • It is rude to take no dumplings when it’s your turn to take.
  • It is rude to take more than 3 dumplings when it’s your turn to take.
  • It is rude to take the last dumpling.

Suppose there are 15 dumplings on the plate and it’s Ang’s turn to take. How many dumplings should he take? Who ends up with the last dumpling?

Birthday Challenge

Albert and Bernard just became friends with Cheryl, and they want to know her birthday. Cheryl gives them a list of 10 possible dates:

May 15 May 16 May 19
June 17 June 18  
July 14 July 16  
August 14 August 15 August 17

Cheryl then tells Albert the month, and Bernard the day.

  • Albert: I don’t know the birthday, but I know that Bernard also doesn’t know.
  • Bernard: At first I didn’t know the birthday, but now I know.
  • Albert: Then I also know the birthday now.

What is Cheryl’s birthday?

The Riddler’s Challenge

Batman, Robin, and Alfred wake up tied to chairs. They each have a number on their forehead. They can’t see their own numbers, but they can see each others’.

The Riddler’s voice pipes in from the intercom: “I’ve put a positive integer on each of your foreheads. Two of the numbers add up to the third. If any of you can guess your own number, you’re all free to go. But if any of you guess wrong, Gotham City is blowing up!”

Batman starts by saying, “I don’t know my number.” Robin then says, “Neither do I.” Then finally, Alfred, “Nor I.” But after a few seconds, Batman says, “I now know my number!”

If Robin’s number was 20 and Alfred’s 30, what number did Batman have?