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?
  • Move a Match
    problem

    Move a Match

    Age
    7 to 11
    Challenge level
    How can you arrange these 10 matches in four piles so that when you move one match from three of the piles into the fourth, you end up with the same arrangement?
  • 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?
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