Reasoning, convincing and proving

  • Knights and Knaves
    problem

    Knights and knaves

    Age
    11 to 14
    Challenge level
    filled star filled star filled star
    Knights always tell the truth. Knaves always lie. Can you catch these knights and knaves out?
  • Distinct Diagonals
    problem

    Distinct diagonals

    Age
    11 to 14
    Challenge level
    filled star empty star empty star
    Weekly Problem 21 - 2010
    How many diagonals can you draw on this square...
  • Square LCM
    problem

    Square LCM

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

    Using the hcf and lcf of the numerators, can you deduce which of these fractions are square numbers?

  • Weekly Lies
    problem

    Weekly lies

    Age
    11 to 14
    Challenge level
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    Mr Ross tells truths or lies depending on the day of the week. Can you catch him out?
  • Three Dice
    problem

    Three dice

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

    Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?

  • Tower of Hanoi
    problem

    Tower of Hanoi

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

    The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.

  • The clue is in the question
    problem

    The clue is in the question

    Age
    16 to 18
    Challenge level
    filled star filled star empty star
    Starting with one of the mini-challenges, how many of the other mini-challenges will you invent for yourself?
  • Cyclic Quadrilaterals
    problem

    Cyclic quadrilaterals

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

    Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?

  • Times of Day
    problem

    Times of day

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

    These pictures show some different activities that you may get up to during a day. What order would you do them in?

  • Strike it out
    problem

    Strike it out

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

    Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.