Permutations

  • Chances are
    problem
    Favourite

    Chances Are

    Age
    14 to 16
    Challenge level

    Which of these games would you play to give yourself the best possible chance of winning a prize?

  • Flagging
    problem

    Flagging

    Age
    11 to 14
    Challenge level
    How many tricolour flags are possible with 5 available colours such that two adjacent stripes must NOT be the same colour. What about 256 colours?
  • Bell Ringing
    problem

    Bell Ringing

    Age
    11 to 14
    Challenge level
    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?
  • Painting Cubes
    problem

    Painting Cubes

    Age
    11 to 14
    Challenge level
    Imagine you have six different colours of paint. You paint a cube using a different colour for each of the six faces. How many different cubes can be painted using the same set of six colours?
  • Placeholder: several colourful numbers
    problem

    Ip?

    Age
    16 to 18
    Challenge level
    Seventh challenge cipher
  • Euromaths
    problem

    Euromaths

    Age
    11 to 14
    Challenge level

    How many ways can you write the word EUROMATHS by starting at the top left hand corner and taking the next letter by stepping one step down or one step to the right in a 5×5 array?

  • And so on and so on
    problem

    And so on and so On

    Age
    11 to 14
    Challenge level

    If you wrote all the possible four digit numbers made by using each of the digits 2, 4, 5, 7 once, what would they add up to?

  • Colourful Tiles
    problem

    Colourful Tiles

    Age
    11 to 14
    Challenge level

    Weekly Problem 21 - 2011
    How many ways can you paint this wall with four different colours?

  • Master Minding
    problem

    Master Minding

    Age
    11 to 14
    Challenge level

    Your partner chooses two beads and places them side by side behind a screen. What is the minimum number of guesses you would need to be sure of guessing the two beads and their positions?

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