Maths problem October 2014

22 October 2014

Hello everyone,

I have three fantastic logic problems for you to work on with your students.

  1. There are five pirates on a ship who have just plundered 100 gold coins. The pirates are ranked in order of seniority, with the captain being ranked 1. The captain must decide how to divide the coins up, then all five will vote on whether to accept the decision. If fewer than half vote 'yes' then the captain is thrown overboard and the process repeats with pirate #2 deciding on the division. The pirates have the following priorities, with 1 being their highest priority and 3 being their lowest priority:

    i) Staying alive

    ii) If they can stay alive either way, they'll act in a way that gets them the most coins

    iii) If they get the same amount of coins either way, they'll vote to kill the captain (or acting captain)

    What is the maximum number of coins that the captain can keep for himself?

  2. Four explorers arrive at a creaky rope bridge in the middle of the night. They only have one torch between them. The bridge is only strong enough to hold two people. If anyone tries to walk across the bridge without the torch they'll fall into the ravine. The explorers can all walk at different speeds. One can walk across in one minute, another in two minutes, another in five minutes and another in ten minutes. How can they all get across the bridge in seventeen minutes without anyone falling in?

  3. Three philosophers are sat on a hill and fall asleep. While they're sleeping someone sneaks up and writes 'idiot' on all of their foreheads. When they wake up, they all start laughing, because they can all see at least one person with 'idiot' written on their foreheads. There are no mirrors and no way of physically checking their own foreheads. Eventually, the most intelligent one stops laughing. Why?

We'd love to hear solutions and explanations from your students. Tweet us @createatest


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