Working systematically

  • Spread
    problem

    Spread

    Age
    16 to 18
    Challenge level
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    Given the mean and standard deviation of a set of marks, what is the greatest number of candidates who could have scored 100%?

  • Late Again
    problem

    Late again

    Age
    5 to 7
    Challenge level
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    Moira is late for school. What is the shortest route she can take from the school gates to the entrance?
  • Nineteen Hexagons
    problem

    Nineteen hexagons

    Age
    5 to 7
    Challenge level
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    In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?
  • Cuisenaire Counting
    problem

    Cuisenaire counting

    Age
    5 to 7
    Challenge level
    filled star empty star empty star

    Here are some rods that are different colours. How could I make a yellow rod using white and red rods?

  • Arrangements
    problem

    Arrangements

    Age
    7 to 11
    Challenge level
    filled star empty star empty star
    Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?
  • Stars
    problem

    Stars

    Age
    11 to 14
    Challenge level
    filled star filled star empty star

    Can you work out what step size to take to ensure you visit all the dots on the circle?

  • Isosceles Triangles
    problem

    Isosceles triangles

    Age
    11 to 14
    Challenge level
    filled star empty star empty star

    Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

  • Efficient cutting
    problem

    Efficient cutting

    Age
    11 to 14
    Challenge level
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    Use a single sheet of A4 paper and make a cylinder having the greatest possible volume. The cylinder must be closed off by a circle at each end.

  • Consecutive Seven
    problem

    Consecutive seven

    Age
    11 to 14
    Challenge level
    filled star empty star empty star

    Can you arrange these numbers into 7 subsets, each of three numbers, so that when the numbers in each are added together, they make seven consecutive numbers?

  • Where to Land
    problem

    Where to land

    Age
    14 to 16
    Challenge level
    filled star filled star empty star

    Chris is enjoying a swim but needs to get back for lunch. How far along the bank should she land?