Combinations

  • 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?
  • Brailler
    problem

    Brailler

    Age
    11 to 14
    Challenge level
    The machine I use to produce Braille messages is faulty and one of the pins that makes a raised dot is not working. I typed a short message in Braille. Can you work out what it really says?
  • 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?
  • Octa Space
    problem

    Octa Space

    Age
    7 to 11
    Challenge level
    In the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?
  • Homes
    problem

    Homes

    Age
    5 to 7
    Challenge level

    Six new homes are being built! They can be detached, semi-detached or terraced houses. How many different combinations of these can you find?

  • Red Express Train
    problem

    Red Express Train

    Age
    5 to 7
    Challenge level
    The Red Express Train usually has five red carriages. How many ways can you find to add two blue carriages?
  • The School Trip
    problem

    The School Trip

    Age
    5 to 7
    Challenge level
    Lorenzie was packing his bag for a school trip. He packed four shirts and three pairs of pants. "I will be able to have a different outfit each day", he said. How many days will Lorenzie be away?
  • Fair Exchange
    problem

    Fair Exchange

    Age
    5 to 7
    Challenge level

    In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?

  • What Shape and Colour?
    problem

    What Shape and Colour?

    Age
    5 to 7
    Challenge level

    Can you fill in the empty boxes in the grid with the right shape and colour?

  • Button-Up
    problem

    Button-Up

    Age
    5 to 7
    Challenge level

    My coat has three buttons. How many ways can you find to do up all the buttons?

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