Reasoning, convincing and proving

  • Digital Book
    problem

    Digital book

    Age
    11 to 14
    Challenge level
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    If it takes 852 digits to number all the pages of a book, what is the number of the last page?
  • Multiplication Magic Square
    problem

    Multiplication magic square

    Age
    11 to 14
    Challenge level
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    Weekly Problem 32 - 2015
    Can you work out the missing numbers in this multiplication magic square?
  • Mini Cross-Number
    problem

    Mini cross-number

    Age
    11 to 14
    Challenge level
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    Which digit replaces x in this crossnumber?
  • The London Eye
    problem

    The London Eye

    Age
    14 to 16
    Challenge level
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    The 80 spokes of The London Eye are made from 4 miles of cable. What is the approximate circumference of the wheel?

  • Would you like a Jelly Baby?
    problem

    Would you like a jelly baby?

    Age
    11 to 14
    Challenge level
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    What is the smallest number of jelly babies Tom must take, to be certain that he gets at least one of each flavour?
  • Would You Rather?
    problem

    Would you rather?

    Age
    7 to 11
    Challenge level
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    Would you rather: Have 10% of £5 or 75% of 80p? Be given 60% of 2 pizzas or 26% of 5 pizzas?

  • Strange Bank Account
    problem

    Strange bank account

    Age
    11 to 14
    Challenge level
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    Imagine a very strange bank account where you are only allowed to do two things...

  • Magical Products
    problem

    Magical products

    Age
    11 to 14
    Challenge level
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    Can you place the nine cards onto a 3x3 grid such that every row, column and diagonal has a product of 1?
  • Perimeter Possibilities
    problem

    Perimeter possibilities

    Age
    11 to 14
    Challenge level
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    I'm thinking of a rectangle with an area of 24. What could its perimeter be?

  • Placeholder: several colourful numbers
    article

    Binomial coefficients

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