Powers and roots

  • Archimedes and numerical roots
    problem

    Archimedes and Numerical Roots

    Age
    14 to 16
    Challenge level
    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?
  • Rachel's Problem
    problem

    Rachel's Problem

    Age
    14 to 16
    Challenge level
    Is it true that $99^n$ has 2n digits and $999^n$ has 3n digits? Investigate!
  • Deep Roots
    problem

    Deep Roots

    Age
    14 to 16
    Challenge level
    Find integer solutions to: $\sqrt{a+b\sqrt{x}} + \sqrt{c+d.\sqrt{x}}=1$
  • Lastly - well
    problem

    Lastly - Well

    Age
    11 to 14
    Challenge level
    What are the last two digits of 2^(2^2003)?
  • Bina-ring
    problem

    Bina-Ring

    Age
    16 to 18
    Challenge level
    Investigate powers of numbers of the form (1 + sqrt 2).
  • problem

    St Ives

    Age
    7 to 14
    Challenge level

    How many were going to St Ives?

  • Largest Number
    problem

    Largest Number

    Age
    11 to 14
    Challenge level

    What is the largest number you can make using the three digits 2, 3 and 4 in any way you like, using any operations you like? You can only use each digit once.

  • Small tomato seedlings in pink pots.
    problem

    Maundy Money

    Age
    11 to 14
    Challenge level

    How much money did the Queen give away in pence as a power of 2?

  • Small tomato seedlings in pink pots.
    problem

    Age of Augustus

    Age
    11 to 14
    Challenge level

    The English mathematician Augustus de Morgan has given his age in algebraic terms. Can you work out when he was born?

  • eNRICHing experience
    problem

    eNRICHing Experience

    Age
    14 to 16
    Challenge level

    Find the five distinct digits N, R, I, C and H in the following nomogram

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