Reasoning, convincing and proving

  • Skeleton Shapes
    problem

    Skeleton shapes

    Age
    5 to 7
    Challenge level
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    How many balls of modelling clay and how many straws does it take to make these skeleton shapes?

  • Square Corners
    problem

    Square corners

    Age
    7 to 11
    Challenge level
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    What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

  • Shopping Basket
    problem

    Shopping basket

    Age
    11 to 16
    Challenge level
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    The items in the shopping basket add and multiply to give the same amount. What could their prices be?

  • Reach 100
    problem

    Reach 100

    Age
    7 to 11
    Challenge level
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    Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

  • Thirty Nine, Seventy Five
    problem

    Thirty nine, seventy five

    Age
    11 to 14
    Challenge level
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    We have exactly 100 coins. There are five different values of coins. We have decided to buy a piece of computer software for 39.75. We have the correct money, not a penny more, not a penny less! Can you discover what the five different types of coins are worth and how many of each we have saved?
  • Disappearing square
    problem

    Disappearing square

    Age
    11 to 14
    Challenge level
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    Do you know how to find the area of a triangle? You can count the squares. What happens if we turn the triangle on end? Press the button and see. Try counting the number of units in the triangle now. Do you have any interesting findings to report?
  • More Mathematical Mysteries
    problem

    More mathematical mysteries

    Age
    11 to 14
    Challenge level
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    Write down a three-digit number Change the order of the digits to get a different number Find the difference between the two three digit numbers Follow the rest of the instructions then try to explain why this works.
  • The Genie in the Jar
    problem

    The genie in the jar

    Age
    11 to 14
    Challenge level
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    This jar used to hold perfumed oil. It contained enough oil to fill granid silver bottles. Each bottle held enough to fill ozvik golden goblets and each goblet held enough to fill vaswik crystal spoons. Each day a spoonful was used to perfume the bath of a beautiful princess. For how many days did the whole jar last? The genie's master replied: Five hundred and ninety five days. What three numbers do the genie's words granid, ozvik and vaswik stand for?
  • Is it Magic or is it Maths?
    problem

    Is it magic or is it maths?

    Age
    11 to 14
    Challenge level
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    Here are three 'tricks' to amaze your friends. But the really clever trick is explaining to them why these 'tricks' are maths not magic. Like all good magicians, you should practice by trying them. Can you explain how they work?
  • Cross-Country Race
    problem

    Cross-country race

    Age
    14 to 16
    Challenge level
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    Eight children enter the autumn cross-country race at school. How many possible ways could they come in at first, second and third places?