Working systematically

  • Triangles to Tetrahedra
    problem

    Triangles to tetrahedra

    Age
    11 to 14
    Challenge level
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    Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

  • Penta Primes
    problem

    Penta primes

    Age
    7 to 11
    Challenge level
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    Using all ten cards from 0 to 9, rearrange them to make five prime numbers. Can you find any other ways of doing it?
  • problem

    Two primes make one square

    Age
    7 to 11
    Challenge level
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    Can you make square numbers by adding two prime numbers together?

  • Seven Square Numbers
    problem

    Seven square numbers

    Age
    7 to 11
    Challenge level
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    Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.
  • The Third Dimension
    problem

    The third dimension

    Age
    5 to 11
    Challenge level
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    Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?

  • 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?

  • problem

    Factor lines

    Age
    7 to 14
    Challenge level
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    Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

  • 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?

  • problem

    Multiplication squares

    Age
    7 to 11
    Challenge level
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    Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

  • 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.