Being resilient

  • Isosceles Seven
    problem

    Isosceles seven

    Age
    14 to 16
    Challenge level
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    Is it possible to find the angles in this rather special isosceles triangle?

  • Expenses
    problem

    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?

  • Fair Shares?
    problem

    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?

  • In a box
    problem

    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?

  • LCM Sudoku
    problem

    LCM Sudoku

    Age
    14 to 16
    Challenge level
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    Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.

  • Speeding boats
    problem

    Speeding boats

    Age
    14 to 16
    Challenge level
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    Two boats travel up and down a lake. Can you picture where they will cross if you know how fast each boat is travelling?

  • Partly Painted Cube
    problem

    Partly painted cube

    Age
    14 to 16
    Challenge level
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    Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?

  • Filling the gaps
    problem

    Filling the gaps

    Age
    14 to 16
    Challenge level
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    Which numbers can we write as a sum of square numbers?

  • Which list is which?
    problem

    Which list is which?

    Age
    14 to 16
    Challenge level
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    Six samples were taken from two distributions but they got muddled up. Can you work out which list is which?

  • Odds and Evens made fair
    problem

    Odds and evens made fair

    Age
    14 to 16
    Challenge level
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    In this follow-up to the problem Odds and Evens, we invite you to analyse a probability situation in order to find the general solution for a fair game.