Reasoning, convincing and proving

  • All in a jumble
    problem

    All in a jumble

    Age
    11 to 14
    Challenge level
    filled star filled star empty star
    My measurements have got all jumbled up! Swap them around and see if you can find a combination where every measurement is valid.
  • A long time at the till
    problem

    A long time at the till

    Age
    14 to 18
    Challenge level
    filled star filled star filled star
    Try to solve this very difficult problem and then study our two suggested solutions. How would you use your knowledge to try to solve variants on the original problem?
  • What Do you Need?
    problem

    What do you need?

    Age
    7 to 11
    Challenge level
    filled star empty star empty star
    Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?
  • Cows and Sheep
    problem

    Cows and sheep

    Age
    7 to 11
    Challenge level
    filled star empty star empty star
    Use your logical reasoning to work out how many cows and how many sheep there are in each field.
  • A Bag of Marbles
    problem

    A bag of marbles

    Age
    5 to 7
    Challenge level
    filled star filled star empty star
    Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?
  • Road maker 2
    problem

    Road maker 2

    Age
    16 to 18
    Challenge level
    filled star filled star filled star
    Can you work out where the blue-and-red brick roads end?
  • Impossible triangles?
    problem

    Impossible triangles?

    Age
    16 to 18
    Challenge level
    filled star filled star empty star
    Which of these triangular jigsaws are impossible to finish?
  • Road maker
    problem

    Road maker

    Age
    14 to 18
    Challenge level
    filled star empty star empty star
    Which of these roads will satisfy a Munchkin builder?
  • Impossible square?
    problem

    Impossible square?

    Age
    16 to 18
    Challenge level
    filled star filled star empty star
    Can you make a square from these triangles?