Creating and manipulating expressions and formulae

  • Semi-Square
    problem

    Semi-Square

    Age
    14 to 16
    Challenge level
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    What is the ratio of the area of a square inscribed in a semicircle to the area of the square inscribed in the entire circle?
  • Chocolate Maths
    problem

    Chocolate Maths

    Age
    11 to 14
    Challenge level
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    Pick the number of times a week that you eat chocolate. This number must be more than one but less than ten. Multiply this number by 2. Add 5 (for Sunday). Multiply by 50... Can you explain why it works?

  • Why 8?
    problem

    Why 8?

    Age
    11 to 14
    Challenge level
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    Choose any four consecutive even numbers. Multiply the two middle numbers together. Multiply the first and last numbers. Now subtract your second answer from the first. Try it with your own numbers. Why is the answer always 8?

  • 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.

  • No Matter
    problem

    No Matter

    Age
    11 to 14
    Challenge level
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    After performing some operations, what number is your answer always a multiple of?

  • Nine, Ten and One
    problem

    Nine, Ten and One

    Age
    11 to 14
    Challenge level
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    Can you find the value of t in these equations?

  • Multiply the Addition Square
    problem

    Multiply the Addition Square

    Age
    11 to 14
    Challenge level
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    If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?

  • Carry Over
    problem

    Carry Over

    Age
    11 to 14
    Challenge level
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    Each letter stands for a different digit, and S is non-zero. Which letter has the lowest value?

  • In Sum-mary
    problem

    In Sum-Mary

    Age
    11 to 14
    Challenge level
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    What does the sum of these three numbers tell us about their product?

  • The Simple Life
    problem

    The Simple Life

    Age
    11 to 14
    Challenge level
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    The answer is $5x+8y$... What was the question?