Prime numbers

  • Factors and Multiples Puzzle
    problem
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    Factors and Multiples Puzzle

    Age
    11 to 14
    Challenge level

    Using your knowledge of the properties of numbers, can you fill all the squares on the board?

  • Four playing cards on top of each other. Each card shows a different ace.
    problem
    Favourite

    Snappy Statements

    Age
    11 to 14
    Challenge level

    Use properties of numbers to work out whether you can satisfy all these statements at the same time.

  • One to Eight
    problem
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    One to Eight

    Age
    11 to 14
    Challenge level

    Complete the following expressions so that each one gives a four digit number as the product of two two digit numbers and uses the digits 1 to 8 once and only once.

  • Why 24?
    problem
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    Why 24?

    Age
    14 to 16
    Challenge level

    Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.

  • Fac-Finding
    problem
    Favourite

    Fac-Finding

    Age
    14 to 16
    Challenge level

    Lyndon chose this as one of his favourite problems. It is accessible but needs some careful analysis of what is included and what is not. A systematic approach is really helpful.

  • Em'power'ed
    problem
    Favourite

    Em'power'ed

    Age
    16 to 18
    Challenge level

    Find the smallest numbers a, b, and c such that: a^2 = 2b^3 = 3c^5 What can you say about other solutions to this problem?

  • Some Cubes
    problem

    Some Cubes

    Age
    16 to 18
    Challenge level
    The sum of the cubes of two numbers is 7163. What are these numbers?
  • Strange Numbers
    problem

    Strange Numbers

    Age
    11 to 14
    Challenge level
    All strange numbers are prime. Every one digit prime number is strange and a number of two or more digits is strange if and only if so are the two numbers obtained from it by omitting either its first or its last digit. Find all strange numbers.
  • Prime counter
    problem

    Prime Counter

    Age
    16 to 18
    Challenge level
    A short challenge concerning prime numbers.
  • Thirty Six Exactly
    problem

    Thirty Six Exactly

    Age
    11 to 14
    Challenge level
    The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
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