Conjecturing and generalising

  • Got \It for Two
    game

    Got It for Two

    Age
    7 to 14
    Challenge level
    2 out of 3

    Got It game for an adult and child. How can you play so that you know you will always win?

  • Steps to the Podium
    problem

    Steps to the Podium

    Age
    7 to 14
    Challenge level
    3 out of 3

    It starts quite simple but great opportunities for number discoveries and patterns!

  • Nim-like Games
    game

    Nim-Like Games

    Age
    7 to 16
    Challenge level
    1 out of 3

    A collection of games on the NIM theme

  • Pentanim
    game

    Pentanim

    Age
    7 to 16
    Challenge level
    2 out of 3

    A game for 2 players with similarities to NIM. Place one counter on each spot on the games board. Players take it is turns to remove 1 or 2 adjacent counters. The winner picks up the last counter.

  • Chocolate Maths
    problem

    Chocolate Maths

    Age
    11 to 14
    Challenge level
    1 out of 3

    Pick the number of times a week that you eat chocolate. This number must be more than one but less than ten. Multiply this number by 2. Add 5 (for Sunday). Multiply by 50... Can you explain why it works?

  • Dicing with numbers
    problem

    Dicing With Numbers

    Age
    11 to 14
    Challenge level
    1 out of 3

    In how many ways can you arrange three dice side by side on a surface so that the sum of the numbers on each of the four faces (top, bottom, front and back) is equal?

  • Threesomes
    problem

    Threesomes

    Age
    11 to 14
    Challenge level
    1 out of 3

    Imagine an infinitely large sheet of square dotty paper on which you can draw triangles of any size you wish (providing each vertex is on a dot). What areas is it/is it not possible to draw?

  • Dotty triangles
    problem

    Dotty Triangles

    Age
    11 to 14
    Challenge level
    1 out of 3

    Imagine an infinitely large sheet of square dotty paper on which you can draw triangles of any size you wish (providing each vertex is on a dot). What areas is it/is it not possible to draw?

  • Small pepper seedlings in turquoise pots.
    problem

    Bishop's Paradise

    Age
    11 to 14
    Challenge level
    1 out of 3

    Which of the statements about diagonals of polygons is false?

  • Sum Equals Product
    problem

    Sum Equals Product

    Age
    11 to 14
    Challenge level
    2 out of 3

    The sum of the numbers 4 and 1 [1/3] is the same as the product of 4 and 1 [1/3]; that is to say 4 + 1 [1/3] = 4 × 1 [1/3]. What other numbers have the sum equal to the product and can this be so for any whole numbers?