Combinatorics

  • Scratch Cards
    problem

    Scratch Cards

    Age
    14 to 16
    Challenge level

    To win on a scratch card you have to uncover three numbers that add up to more than fifteen. What is the probability of winning a prize?

  • Snooker
    problem

    Snooker

    Age
    16 to 18
    Challenge level

    A player has probability 0.4 of winning a single game. What is his probability of winning a 'best of 15 games' tournament?

  • Magic W Wrap Up
    problem

    Magic W Wrap Up

    Age
    16 to 18
    Challenge level

    Prove that you cannot form a Magic W with a total of 12 or less or with a with a total of 18 or more.

  • Cube Net
    problem

    Cube Net

    Age
    16 to 18
    Challenge level

    How many tours visit each vertex of a cube once and only once? How many return to the starting point?

  • Factorial Fun
    problem

    Factorial Fun

    Age
    16 to 18
    Challenge level

    How many divisors does factorial n (n!) have?

  • Stage 5 Cipher Challenge
    problem

    Stage 5 Cipher Challenge

    Age
    16 to 18
    Challenge level

    Can you crack these very difficult challenge ciphers? How might you systematise the cracking of unknown ciphers?

  • Links and Knots
    article

    Links and Knots

    Some puzzles requiring no knowledge of knot theory, just a careful inspection of the patterns. A glimpse of the classification of knots, prime knots, crossing numbers and knot arithmetic.
  • The Eternity Puzzle
    article

    The Eternity Puzzle

    A big prize was offered for solving The Eternity Puzzle, a jigsaw with no picture and every piece is the same on both sides. The finished result forms a regular dodecagon (12 sided polygon).
  • Tangles
    article

    Tangles

    A personal investigation of Conway's Rational Tangles. What were the interesting questions that needed to be asked, and where did they lead?
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