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King's Maths School

Challenge 455: One question

How many questions will get the information you need?

You are a xenoanthropologist studying the alien planet of Mintaka IV. On Mintaka IV, there are two species of aliens - Xorts and Yokks - and there are two continents - Algorf and Blorgon.

Xorts from Algorf always tell the truth, while Xorts from Blorgon always lie. On the other hand, Yokks from Algorf always lie, while Yokks from Blorgon always tell the truth.

You are speaking to a group of 13 aliens, but you don't know what species they are or where they're from.

You ask each of them "are you a Xort?" and 8 say "yes". 

You ask each of them "are you from Algorf" and 5 say "yes".

You ask them another question - to which the answer can only be yes or no - and 4 say "yes". On the basis of this information, you are able to deduce the species and continent of each alien.

What question might you have asked, and how many are Yokks from Blorgon?

(There are many possible answers to this question - you might like to submit more than one!)

Submit your solution

Please do send in your solution to this problem to weeklymaths@kcl.ac.uk You can scan or photograph your written work, or type your solutions. If this is your first weekly maths challenge solution, please include your year group and the name of the school you attend. We'll be happy to provide feedback on your solution, assuming that you are in year 11 or below. If you are older than this, we hope you enjoy trying the problems and reviewing your solutions against those we publish on the website.