Powers and roots

  • Like Powers
    problem

    Like Powers

    Age
    11 to 14
    Challenge level
    Investigate $1^n + 19^n + 20^n + 51^n + 57^n + 80^n + 82^n $ and $2^n + 12^n + 31^n + 40^n + 69^n + 71^n + 85^n$ for different values of n.
  • Two Many
    problem

    Two Many

    Age
    11 to 14
    Challenge level
    What is the least square number which commences with six two's?
  • Lost in Space
    problem

    Lost in Space

    Age
    14 to 16
    Challenge level
    How many ways are there to count 1 - 2 - 3 in the array of triangular numbers? What happens with larger arrays? Can you predict for any size array?
  • 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.

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