Diophantine equations

  • Letter Land
    problem
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    Letter Land

    Age
    11 to 14
    Challenge level
    If: A + C = A; F x D = F; B - G = G; A + H = E; B / H = G; E - G = F and A-H represent the numbers from 0 to 7 Find the values of A, B, C, D, E, F and H.
  • Fibs
    problem
    Favourite

    Fibs

    Age
    11 to 14
    Challenge level
    The well known Fibonacci sequence is 1 ,1, 2, 3, 5, 8, 13, 21.... How many Fibonacci sequences can you find containing the number 196 as one of the terms?
  • CD Heaven
    problem
    Favourite

    CD Heaven

    Age
    14 to 16
    Challenge level

    All CD Heaven stores were given the same number of a popular CD to sell for £24. In their two week sale each store reduces the price of the CD by 25% ... How many CDs did the store sell at each price?

  • Rudolff's Problem
    problem

    Rudolff's Problem

    Age
    14 to 16
    Challenge level
    A group of 20 people pay a total of £20 to see an exhibition. The admission price is £3 for men, £2 for women and 50p for children. How many men, women and children are there in the group?
  • Some Cubes
    problem

    Some Cubes

    Age
    16 to 18
    Challenge level
    The sum of the cubes of two numbers is 7163. What are these numbers?
  • Double Angle Triples
    problem

    Double Angle Triples

    Age
    16 to 18
    Challenge level
    Try out this geometry problem involving trigonometry and number theory
  • Lattice Points
    problem

    Lattice Points

    Age
    16 to 18
    Challenge level
    Why are there only a few lattice points on a hyperbola and infinitely many on a parabola?
  • Coffee
    problem

    Coffee

    Age
    14 to 16
    Challenge level
    To make 11 kilograms of this blend of coffee costs £15 per kilogram. The blend uses more Brazilian, Kenyan and Mocha coffee... How many kilograms of each type of coffee are used?
  • In particular
    problem

    In Particular

    Age
    14 to 16
    Challenge level
    Can you find formulas giving all the solutions to 7x + 11y = 100 where x and y are integers?
  • Are you kidding
    problem

    Are You Kidding

    Age
    14 to 16
    Challenge level
    If the altitude of an isosceles triangle is 8 units and the perimeter of the triangle is 32 units.... What is the area of the triangle?
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