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Ridiculously difficult looking challenges

November 2, 2015

A while back, I posed a challenge to my (then) year 10 class about using their index notation knowledge to solve a “ridiculously difficult” question. I can’t remember exactly what it was but it looked a bit like this:

Simplify Indices

The hope was to create something that looked very daunting and difficult but actually isn’t that hard. I occasionally like to play up something along the lines of, “Hey guys, I’ve got some questions for you to do today. I also have one that there’s no way you’ll be able to do but you probably don’t want to see that do you?” Then, I’ll flash it under the visualiser long enough for them to see it and see that it looks difficult. Then I take it away, “See, no chance…… Well…. I suppose there’s no harm leaving it there if you really want to give it a go.”

You can probably imagine what happens. It’s great to have another more horrid one for when someone completes it so you can say, “No way! Are you serious? I don’t believe you, let me see. Right, well in that case, try this then!” However, you probably don’t want to spin it out to more than two as it gets annoying (so I’m readily told).

Well, I have a new year 10 class. They are coming up to solving equations and the questions can get a bit repetitive so I thought I’d create a couple more similar questions. Here they are:

Equation 1

Equation 2

Anyway, I always thought it was a good approach and a nice thing to do sometimes, but perhaps unsurprisingly, there aren’t many ready made questions like these. I’ve been meaning to make more for ages but obviously haven’t really got round to making many so I thought twitter and this blog’s lovely readers might help.

If you’d like to contribute, please make up a question, take a picture and tweet it to me (@reflectivemaths). I’ll find a way to collate them and share.

Some guidelines:

  • Looks horribly complex
  • Actually isn’t
  • Isn’t too tedious to work through
  • GCSE level
  • By sending me the picture, you’re happy for me to use and share it in a not-for-profit way

I also think there’s scope for a newspaper to pick these things up as daily puzzles. Sudoku is popular so I don’t see why these wouldn’t be right?

EDIT here’s another one I’ve made


EDIT Here are some submissions:

challenging questions solve my maths

these two are from @solvemymaths

challenging questions beveridge

This one from @icecolbeverage with the task of finding Tan EAC

Also, @MrMattock sent me this link to a vectors related question activity


From → Uncategorized

  1. One of my Russian colleagues told his PhD student to try a book by Skanavi, titled “сборник задач по математике для поступающик во втузы”, which translates roughly to “Problems in mathematics for technical college applicants”. It’s full of hundreds and hundreds of these kinds of problems that look incredibly complex. Unfortunately, because it’s Russian, they’re often very hard to solve. But they always reduce down to something very simple. I’ve finally tracked down a link to download this book, from a very sketchy-looking Russian site:
    The book was produced in Soviet times, so don’t feel bad about pirating it – property is theft, comrade!
    One of our other, English, lecturers used to set a few questions of the “simplify this fraction” sort that you have above for his first-year students. You’d have to use every trick in the book to find they eventually reduce down to either 0 or 1.

    • That’s an interesting find thanks.
      Don’t suppose you have access to one of the simplifiable fractions do you?

  2. Nice Idea – what about using difference of two squares questions like:

    (53^2 – 47^2)^2

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