Creating and manipulating expressions and formulae

  • Powers of Four
    problem

    Powers of Four

    Age
    14 to 16
    Challenge level
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    Can you work out the value of x in this 'power-full' equation?

  • Magic W
    problem

    Magic W

    Age
    14 to 16
    Challenge level
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    Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.

  • Consecutive Squares
    problem

    Consecutive Squares

    Age
    14 to 16
    Challenge level
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    The squares of any 8 consecutive numbers can be arranged into two sets of four numbers with the same sum. True of false?

  • Janine's Conjecture
    problem

    Janine's Conjecture

    Age
    14 to 16
    Challenge level
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    Janine noticed, while studying some cube numbers, that if you take three consecutive whole numbers and multiply them together and then add the middle number of the three, you get the middle number. Does this always work? Can you prove or disprove this conjecture?

  • Hand Swap
    problem

    Hand Swap

    Age
    14 to 16
    Challenge level
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    My train left London between 6 a.m. and 7 a.m. and arrived in Paris between 9 a.m. and 10 a.m. At the start and end of the journey the hands on my watch were in exactly the same positions but the minute hand and hour hand had swopped places. What time did the train leave London and how long did the journey take?

  • Never Prime
    problem

    Never Prime

    Age
    14 to 16
    Challenge level
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    If a two digit number has its digits reversed and the smaller of the two numbers is subtracted from the larger, prove the difference can never be prime.

  • Mediant madness
    problem

    Mediant Madness

    Age
    14 to 16
    Challenge level
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    Kyle and his teacher disagree about his test score - who is right?

  • Archimedes and numerical roots
    problem

    Archimedes and Numerical Roots

    Age
    14 to 16
    Challenge level
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    The problem is how did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?

  • Triangles within Squares
    problem

    Triangles Within Squares

    Age
    14 to 16
    Challenge level
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    Can you find a rule which relates triangular numbers to square numbers?

  • Walk the Plank
    problem

    Walk the Plank

    Age
    14 to 16
    Challenge level
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    A rectangular plank fits neatly inside a square frame when placed diagonally. What is the length of the plank?