Working systematically

  • Trebling
    problem

    Trebling

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

    Can you replace the letters with numbers? Is there only one solution in each case?

  • Eggs in Baskets
    problem

    Eggs in baskets

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

    There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. How many eggs are in each basket?

  • Two on Five
    problem

    Two on five

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

    Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?

  • The Pied Piper of Hamelin
    problem

    The Pied Piper of Hamelin

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

    This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

  • Elf Suits
    problem

    Elf suits

    Age
    7 to 11
    Challenge level
    filled star filled star empty star
    If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?
  • 1 to 8
    problem

    1 to 8

    Age
    7 to 11
    Challenge level
    filled star empty star empty star
    Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
  • Eight queens
    problem

    Eight queens

    Age
    7 to 11
    Challenge level
    filled star filled star empty star
    Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.
  • 5 on the clock
    problem

    5 on the clock

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

    On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?

  • Bell Ringing
    problem

    Bell ringing

    Age
    11 to 14
    Challenge level
    filled star filled star empty star
    Suppose you are a bellringer. Can you find the changes so that, starting and ending with a round, all the 24 possible permutations are rung once each and only once?
  • Take a message soldier
    problem

    Take a message soldier

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

    A messenger runs from the rear to the head of a marching column and back. When he gets back, the rear is where the head was when he set off. What is the ratio of his speed to that of the column?