Indices

  • Sums of Squares and Sums of Cubes
    article

    Sums of squares and sums of cubes

    An account of methods for finding whether or not a number can be written as the sum of two or more squares or as the sum of two or more cubes.
  • Learn About Number Bases
    article

    Learn about number bases

    We are used to writing numbers in base ten, using 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Eg. 75 means 7 tens and five units. This article explains how numbers can be written in any number base.
  • Card Shuffle
    article

    Card shuffle

    This article for students and teachers tries to think about how long would it take someone to create every possible shuffle of a pack of cards, with surprising results.
  • Public Key Cryptography
    article

    Public key cryptography

    An introduction to coding and decoding messages and the maths behind how to secretly share information.
  • How Many Solutions?
    problem

    How many solutions?

    Age
    16 to 18
    Challenge level
    filled star empty star empty star
    Find all the solutions to the this equation.
  • Novemberish
    problem

    Novemberish

    Age
    14 to 16
    Challenge level
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    a) A four digit number (in base 10) aabb is a perfect square. Discuss ways of systematically finding this number. (b) Prove that 11^{10}-1 is divisible by 100.
  • A Biggy
    problem

    A biggy

    Age
    14 to 16
    Challenge level
    filled star empty star empty star
    Find the smallest positive integer N such that N/2 is a perfect cube, N/3 is a perfect fifth power and N/5 is a perfect seventh power.
  • Staircase
    problem

    Staircase

    Age
    16 to 18
    Challenge level
    filled star empty star empty star
    Solving the equation x^3 = 3 is easy but what about solving equations with a 'staircase' of powers?