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Fractional puzzle

April 4, 2014

After seeing a blog post here talking about a puzzle tweeted by Colin Beveridge, I thought I’d have a go.
The puzzle is:
xy = 3
x + y = 2
What is the value of 1/x + 1/y ?
Despite @srcav’s beliefs, I do like a good pure maths problem (we just seem to disagree about what counts as good). So I broke out my felt tip pens and here is my working:

If you’ve read the link you’ll know that the quadratic approach leads you into complex numbers. Now, while I can do those, I thought I’d try another approach before going down that route:


It’s quite satisfying that it comes out so nicely. The part in square brackets turned out to be a route I didn’t want to pursue but I quite like leaving my abandoned routes in my working.

So, thanks Colin, that was fairly interesting to have a play with. Thanks to Cav for highlighting it too.


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  1. Am I missing something here?

    Doesn’t 1/x + 1/y = (y+x)/(xy) = 2/3 by using algebraic fractions?

  2. All the above working is mere wasting of time and space!!. Just divide the second equation by the first equation. Thats it. You get the answer!!!!

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