Creating and manipulating expressions and formulae

  • Just touching
    problem

    Just touching

    Age
    16 to 18
    Challenge level
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    Three semi-circles have a common diameter, each touches the other two and two lie inside the biggest one. What is the radius of the circle that touches all three semi-circles?
  • Old Nuts
    problem

    Old nuts

    Age
    16 to 18
    Challenge level
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    In turn 4 people throw away three nuts from a pile and hide a quarter of the remainder finally leaving a multiple of 4 nuts. How many nuts were at the start?
  • Absurdity Again
    problem

    Absurdity again

    Age
    16 to 18
    Challenge level
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    What is the value of the integers a and b where sqrt(8-4sqrt3) = sqrt a - sqrt b?
  • Reaction rates!
    article

    Reaction rates!

    Fancy learning a bit more about rates of reaction, but don't know where to look? Come inside and find out more...
  • Magic squares for special occasions
    article

    Magic squares for special occasions

    This article explains how to make your own magic square to mark a special occasion with the special date of your choice on the top line.
  • Telescoping Functions
    article

    Telescoping functions

    Take a complicated fraction with the product of five quartics top and bottom and reduce this to a whole number. This is a numerical example involving some clever algebra.
  • Price Match
    problem

    Price match

    Age
    7 to 11
    Challenge level
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    Can you find pairs of differently sized windows that cost the same?

  • The Simple Life
    problem

    The simple life

    Age
    11 to 14
    Challenge level
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    The answer is $5x+8y$... What was the question?
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