Mr C Dodd – Staff Editor
Rich and ugly, or poor and pretty?
How many socks make a pair?
There are four pairs of blue socks and three pairs of red socks in a drawer. In the dark, how many socks must you take out of the drawer to be sure of getting a matching pair?
You and nine other individuals have been captured by super intelligent alien overlords. The aliens think humans look quite tasty, but their civilization forbids eating highly logical and cooperative beings. Unfortunately, they’re not sure whether you qualify, so they decide to give you all a test. Through its universal translator, the alien guarding you tells you the following: You will be placed in a single-file line facing forward in size order so that each of you can see everyone lined up ahead of you. You will not be able to look behind you or step out of line. Each of you will have either a black or a white hat on your head assigned randomly, and I won’t tell you how many of each colour there are.
When I say to begin, each of you must guess the colour of your hat starting with the person in the back and moving up the line. And don’t even try saying words other than black or white or signalling some other way, like intonation or volume; you’ll all be eaten immediately. If at least nine of you guess correctly, you’ll all be spared. You have five minutes to discuss and come up with a plan, and then I’ll line you up, assign your hats, and we’ll begin.
Can you think of a strategy guaranteed to save everyone?
Solution: Watch a short TedEd video on YouTube, outlining the solution: Can you solve the prisoner hat riddle?
If you enjoy solving puzzles, Alex Bellos sets a challenging puzzle like this in The Guardian every two weeks.
Oxbridge Interview Questions
How can we estimate the mass of the atmosphere?
What can historians not find out about the past?
The viruses that infect us are totally dependent on human cells for their reproduction; is it therefore surprising that viruses cause human diseases?
Medicine / Biomedical Science
[Click here to learn more about these questions.]
A number of leading courses and institutions require students to complete pre-admission tests as part of the application process. These tests focus on the skills and aptitudes required for higher-level study.
The Language of the Lake
The question is taken from the North American Computational Linguistics Olympiad, a competition for high school students. It’s testing you on the sort of linguistics skills that might help you get a job at a leading technology communication firm like Google. The brightest contestants are able to solve it. If you want to print out the problem, click this link here.
Hint: Isolate all the patterns you can see. Work out which are the likely words for ‘one’, ‘two’, ‘three’, and ‘fish’. And then curse Aymara for its idiosyncrasies!
Solution: click here to see the solution to this difficult problem.