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Which subjects are they studying?

the brainbuster

This competition is now closed.

At Camford University 83% of students study Maths, 72% study Physics and 68% study Chemistry. What is the lowest percentage that could study all three subjects?

Show your reasoning.

the entries

Many thanks to all of you who entered the brainbuster.

This one attracted a good number of entries, most of which were correct.

As ever, the wrong answers were quite illuminating too. One entrant simply did the 'sums' wrongly and was 1% out. Another's answer was 'Nearly 0%', backed up with rather bizarre reasoning. But most entrants found it quite straightforward.

the solution

Here is the answer as provided by our winner:

23%. In order to minimise the percentage of students studying all three subjects, it's necessary to maximise the percentage of students who don't. This is achieved by assuming that non-mathematicians, non-physicists and non-chemists all form non-overlapping groups. The sizes of these groups are 17%, 28% and 32% respectively, totalling 77%. The number of students who study all three is therefore 100-77, or 23%.

and the winner is...

Congratulations to Graham Holmes, who wins £250 of Firebox vouchers.

Graham has a 1st Class (Hons) degree in Electronics from the University of Kent and expertise in electronics, general software, web applications and data analysis. He's also been known to dabble in the occasional maths problem for fun!

Many thanks again to all entrants - do try the next brainbuster!