Working systematically

  • Expenses
    problem
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    Expenses

    Age
    14 to 16
    Challenge level
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    What is the largest number which, when divided into these five numbers in turn, leaves the same remainder each time?

  • Of all the areas
    problem
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    Of All the Areas

    Age
    14 to 16
    Challenge level
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    Can you find a general rule for finding the areas of equilateral triangles drawn on an isometric grid?

  • Fair Shares?
    problem
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    Fair Shares?

    Age
    14 to 16
    Challenge level
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    A mother wants to share some money by giving each child in turn a lump sum plus a fraction of the remainder. How can she do this to share the money out equally?

  • What's Possible?
    problem
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    What's Possible?

    Age
    14 to 16
    Challenge level
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    Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?

  • CD Heaven
    problem
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    CD Heaven

    Age
    14 to 16
    Challenge level
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    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?

  • Tree tops
    problem
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    Tree Tops

    Age
    14 to 16
    Challenge level
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    Can you make sense of information about trees in order to maximise the profits of a forestry company?

  • In a box
    problem
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    In a Box

    Age
    14 to 16
    Challenge level
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    Chris and Jo put two red and four blue ribbons in a box. They each pick a ribbon from the box without looking. Jo wins if the two ribbons are the same colour. Is the game fair?

  • Pick's Theorem
    problem
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    Pick's Theorem

    Age
    14 to 16
    Challenge level
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    Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.

  • Painted Cube
    problem
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    Painted Cube

    Age
    14 to 16
    Challenge level
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    Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?

  • Tetrahedra Tester
    problem

    Tetrahedra Tester

    Age
    14 to 16
    Challenge level
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    An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?