Exploring and noticing

  • Climbing Powers
    problem
    Favourite

    Climbing powers

    Age
    16 to 18
    Challenge level
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    Does it make any difference how we write powers of powers? 

  • Polite Numbers
    problem

    Polite numbers

    Age
    16 to 18
    Challenge level
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    A polite number can be written as the sum of two or more consecutive positive integers, for example 8+9+10=27 is a polite number. Can you find some more polite, and impolite, numbers?
  • What do functions do for tiny x?
    problem

    What do functions do for tiny x?

    Age
    16 to 18
    Challenge level
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    Looking at small values of functions. Motivating the existence of the Maclaurin expansion.

  • It's only a minus sign
    problem
    Favourite

    It's only a minus sign

    Age
    16 to 18
    Challenge level
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    Solve these differential equations to see how a minus sign can change the answer

  • Impossible triangles?
    problem

    Impossible triangles?

    Age
    16 to 18
    Challenge level
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    Which of these triangular jigsaws are impossible to finish?
  • Farey Neighbours
    problem

    Farey neighbours

    Age
    16 to 18
    Challenge level
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    Farey sequences are lists of fractions in ascending order of magnitude. Can you prove that in every Farey sequence there is a special relationship between Farey neighbours?

  • Nine Eigen
    problem

    Nine eigen

    Age
    16 to 18
    Challenge level
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    Explore how matrices can fix vectors and vector directions.

  • Placeholder: several colourful numbers
    problem

    Integral arranging

    Age
    16 to 18
    Challenge level
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    How would you sort out these integrals?