Combinations

  • 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?

  • Teams
    problem
    Favourite

    Teams

    Age
    16 to 18
    Challenge level

    Two brothers belong to a club with 10 members. Four are selected for a match. Find the probability that both brothers are selected.

  • Lesser Digits
    problem

    Lesser Digits

    Age
    11 to 14
    Challenge level
    How many positive integers less than or equal to 4000 can be written down without using the digits 7, 8 or 9?
  • Sam Again
    problem

    Sam Again

    Age
    11 to 14
    Challenge level
    Here is a collection of puzzles about Sam's shop sent in by club members. Perhaps you can make up more puzzles, find formulas or find general methods.
  • Patchwork Quilt
    problem

    Patchwork Quilt

    Age
    7 to 14
    Challenge level
    Squares of the type shown are sewn together to make a quilt. How many different quilts can be made?
  • Cereal Packets
    problem

    Cereal Packets

    Age
    7 to 11
    Challenge level
    How can you put five cereal packets together to make different shapes if you must put them face-to-face?
  • 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?
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