Iteration

  • A Very Shiny Nose?
    problem

    A very shiny nose?

    Age
    16 to 18
    Challenge level
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    This problem explores the biology behind Rudolph's glowing red nose, and introduces the real life phenomena of bacterial quorum sensing.

  • Archimedes Numerical Roots
    problem

    Archimedes numerical roots

    Age
    16 to 18
    Challenge level
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    How did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?
  • Difference Dynamics
    problem

    Difference dynamics

    Age
    14 to 18
    Challenge level
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    Take three whole numbers. The differences between them give you three new numbers. Find the differences between the new numbers and keep repeating this. What happens?
  • Ford Circles
    problem

    Ford circles

    Age
    16 to 18
    Challenge level
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    Can you find the link between these beautiful circle patterns and Farey Sequences?

  • Peaches in General
    problem

    Peaches in general

    Age
    14 to 16
    Challenge level
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    It's like 'Peaches Today, Peaches Tomorrow' but interestingly generalized.
  • Spirostars
    problem

    Spirostars

    Age
    16 to 18
    Challenge level
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    A spiropath is a sequence of connected line segments end to end taking different directions. The same spiropath is iterated. When does it cycle and when does it go on indefinitely?
  • Stretching Fractions
    problem

    Stretching fractions

    Age
    14 to 16
    Challenge level
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    Imagine a strip with a mark somewhere along it. Fold it in the middle so that the bottom reaches back to the top. Stetch it out to match the original length. Now where's the mark?
  • Slippage
    problem

    Slippage

    Age
    14 to 16
    Challenge level
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    A ladder 3m long rests against a wall with one end a short distance from its base. Between the wall and the base of a ladder is a garden storage box 1m tall and 1m high. What is the maximum distance up the wall which the ladder can reach?
  • V-P Cycles
    problem

    V-P cycles

    Age
    16 to 18
    Challenge level
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    Form a sequence of vectors by multiplying each vector (using vector products) by a constant vector to get the next one in the seuence(like a GP). What happens?

  • Dalmatians
    problem

    Dalmatians

    Age
    14 to 18
    Challenge level
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    Investigate the sequences obtained by starting with any positive 2 digit number (10a+b) and repeatedly using the rule 10a+b maps to 10b-a to get the next number in the sequence.