Working systematically

  • Snooker
    problem

    Snooker

    Age
    16 to 18
    Challenge level
    filled star empty star empty star

    A player has probability 0.4 of winning a single game. What is his probability of winning a 'best of 15 games' tournament?

  • Exhaustion
    problem

    Exhaustion

    Age
    16 to 18
    Challenge level
    filled star filled star empty star
    Find the positive integer solutions of the equation (1+1/a)(1+1/b)(1+1/c) = 2
  • Rain or Shine
    problem

    Rain or shine

    Age
    16 to 18
    Challenge level
    filled star filled star empty star

    Predict future weather using the probability that tomorrow is wet given today is wet and the probability that tomorrow is wet given that today is dry.

  • Bendy Quad
    problem

    Bendy quad

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

    Four rods are hinged at their ends to form a convex quadrilateral. Investigate the different shapes that the quadrilateral can take. Be patient this problem may be slow to load.

  • Days and Dates
    problem

    Days and dates

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

    Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

  • Telescoping series
    problem

    Telescoping series

    Age
    16 to 18
    Challenge level
    filled star filled star empty star

    Find $S_r = 1^r + 2^r + 3^r + ... + n^r$ where r is any fixed positive integer in terms of $S_1, S_2, ... S_{r-1}$.

  • Purr-fection
    problem

    Purr-fection

    Age
    16 to 18
    Challenge level
    filled star empty star empty star
    What is the smallest perfect square that ends with the four digits 9009?
  • The Pet Graph
    problem

    The pet graph

    Age
    7 to 11
    Challenge level
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    Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?
  • problem

    Birthday cakes

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

    Jack's mum bought some candles to use on his birthday cakes and when his sister was born, she used them on her cakes too. Can you use the information to find out when Kate was born?

  • Six is the Sum
    problem

    Six is the sum

    Age
    7 to 11
    Challenge level
    filled star filled star empty star
    What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?