Pirate Maths/Logic Puzzles

July 31, 2015 Madeleine K

A logic maths puzzle and solution for intermediate students

This puzzle, and more, can be found at www.mathsisfun.com


5 Pirates Logic Puzzle

5 pirates of different ages have a treasure of 100 gold coins.
On their ship, they decide to split the coins using this scheme:
The oldest pirate proposes how to share the coins, the OTHER pirates (not including the oldest) will vote for or against it.
If 50% or more of the pirates vote for it, then the coins will be shared that way. Otherwise, the pirate proposing the scheme will be thrown overboard, and the process is repeated with the pirates that remain.
Assuming that all 5 pirates are intelligent, rational, greedy, and do not wish to die, (and are rather good at math for pirates) what will happen?



5 Pirates Solution

The oldest pirate will propose a 97 : 0 : 1 : 0 : 2 split.
Let us name the pirates (from oldest to youngest): Alex, Billy, Colin, Duncan and Eddie.
Working backwards: 
2 Pirates: Duncan splits the coins 0: 100 (giving all to Eddie). Otherwise, and perhaps even then, Eddie would vote against him and over he goes!
3 Pirates: Colin splits the coins 99 : 1 : 0. Eddie is going to vote against him no matter what (see above) so gets nothing, but Duncan will vote for him, to get at least one gold out of it (if Duncan votes against him, there will only be two pirates remaining and Duncan will get nothing, and may even lose his life!)
4 Pirates: Billy splits the coins 97 : 0 : 2 : 1. This way, Eddie will vote for him, and so will Duncan - they're getting more than they would under 3 pirates.
5 Pirates: Alex splits the coins 97 : 0 : 1 : 0 : 2. This way, Eddie will vote for him, and so will Colin - they're both getting better than they would under 4 pirates.


background

Have you thought about online lessons?

Online tuition gives you access to brilliant tutors across the country
Connect one-to-one with a tutor or share your lesson with a group for 50% of the tutor's hourly rate! Find a Tutor for One-to-One Find an Online Study Group

Want to know more?

Visit Madeleine's profile to find out more and send a message.

Visit Madeleine's Profile

Resources others found helpful

How to get into medical school

This resource signposts and describes what we should be aiming for in our application to study …

learn more

Dyslexia Symptoms in Teenagers and Adults

Signs and symptoms that suggest dyslexia in teenagers and adults

learn more

Adding and subtracting fractions

This document creates a mini-booklet with simple, step-by-step instructions for adding and …

learn more

Exam Preparation

Getting ready for exams is about more than just being buried in books!
10 

learn more

Free resources, revision notes and past papers for students

Find revision guides, exam papers and sample essays amongst hundreds of free resources available to students.

Find resources any subjects

Maths resources | Science resources | Music resources | Spanish resources | English resources | French resources