Other equations

  • One and three
    problem
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    One and Three

    Age
    14 to 16
    Challenge level

    Two motorboats travelling up and down a lake at constant speeds leave opposite ends A and B at the same instant, passing each other, for the first time 600 metres from A, and on their return, 400 metres from B. How long is the lake?

  • Root to Poly
    problem
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    Root to Poly

    Age
    14 to 16
    Challenge level

    Find the polynomial p(x) with integer coefficients such that one solution of the equation p(x)=0 is $1+\sqrt 2+\sqrt 3$.

  • Two Trees
    problem
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    Two Trees

    Age
    16 to 18
    Challenge level

    Can you find the distance between the two trees using the information given?

  • Polynomial Relations
    problem
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    Polynomial Relations

    Age
    16 to 18
    Challenge level

    Given any two polynomials in a single variable it is always possible to eliminate the variable and obtain a formula showing the relationship between the two polynomials. Try this one.

  • 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?
  • Old Nuts
    problem

    Old Nuts

    Age
    16 to 18
    Challenge level
    In turn 4 people throw away three nuts from a pile and hide a quarter of the remainder finally leaving a multiple of 4 nuts. How many nuts were at the start?
  • 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?
  • How big?
    problem

    How Big?

    Age
    11 to 14
    Challenge level
    If the sides of the triangle in the diagram are 3, 4 and 5, what is the area of the shaded square?
  • Three four five
    problem

    Three Four Five

    Age
    14 to 16
    Challenge level
    Two semi-circles (each of radius 1/2) touch each other, and a semi-circle of radius 1 touches both of them. Find the radius of the circle which touches all three semi-circles.
  • 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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