Number theory

  • Diophantine n-tuples
    problem

    Diophantine N-Tuples

    Age
    14 to 16
    Challenge level
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    Can you explain why a sequence of operations always gives you perfect squares?

  • Really Mr. Bond
    problem

    Really Mr. Bond

    Age
    14 to 16
    Challenge level
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    Can you explain what's happening with these numbers?

  • Data Chunks
    problem

    Data Chunks

    Age
    14 to 16
    Challenge level
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    Data is sent in chunks of two different sizes - a yellow chunk has 5 characters and a blue chunk has 9 characters. A data slot of size 31 cannot be exactly filled with a combination of yellow and blue chunks, explore what sizes near to 31 can, or cannot, be exactly filled.

  • Pythagorean Golden Means
    problem

    Pythagorean Golden Means

    Age
    16 to 18
    Challenge level
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    Show that the arithmetic mean, geometric mean and harmonic mean of a and b can be the lengths of the sides of a right-angles triangle if and only if a = bx^3, where x is the Golden Ratio.

  • Got \It Article
    article

    Got It Article

    This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
  • The Codabar Check
    article

    The Codabar Check

    This article explains how credit card numbers are defined and the check digit serves to verify their accuracy.

  • Placeholder: several colourful numbers
    article

    Binomial Coefficients

    An introduction to the binomial coefficient, and exploration of some of the formulae it satisfies.

  • 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.