Conjecturing and generalising

  • Thank your Lucky Stars
    problem

    Thank Your Lucky Stars

    Age
    14 to 16
    Challenge level

    A counter is placed in the bottom right hand corner of a grid. You toss a coin and move the star according to the following rules: ... What is the probability that you end up in the top left-hand corner of the grid?

  • Overlap
    problem

    Overlap

    Age
    14 to 16
    Challenge level

    A red square and a blue square overlap. Is the area of the overlap always the same?

  • Small pepper seedlings in orange pots.
    problem

    Little Difference

    Age
    14 to 16
    Challenge level

    What is the value of $2015 \times 2017$ - $2016 \times 2016$?

  • Small tomato seedlings in pink pots.
    problem

    Last-But-One

    Age
    14 to 16
    Challenge level

    What is the last-but-one digit of 99! ?

  • Small tomato seedlings in pink pots.
    problem

    Producing an Integer

    Age
    14 to 16
    Challenge level

    Multiply a sequence of n terms together. Can you work out when this product is equal to an integer?

  • Jam
    game

    Jam

    Age
    14 to 16
    Challenge level
    A game for 2 players
  • Jam
    game

    Jam

    Age
    14 to 16
    Challenge level

    To avoid losing think of another very well known game where the patterns of play are similar.

  • Polycircles
    problem

    Polycircles

    Age
    14 to 16
    Challenge level

    Show that for any triangle it is always possible to construct 3 touching circles with centres at the vertices. Is it possible to construct touching circles centred at the vertices of any polygon?

  • Hypotenuse Lattice points
    problem

    Hypotenuse Lattice Points

    Age
    14 to 16
    Challenge level

    The triangle OMN has vertices on the axes with whole number co-ordinates. How many points with whole number coordinates are there on the hypotenuse MN?

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