Conjecturing and generalising

  • Light the Lights
    problem

    Light the lights

    Age
    5 to 7
    Challenge level
    filled star filled star empty star

    Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?

  • Light the Lights Again
    problem

    Light the lights again

    Age
    7 to 11
    Challenge level
    filled star filled star empty star

    Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you work out the rule for each light?

  • Charlie's delightful machine
    problem

    Charlie's delightful machine

    Age
    11 to 16
    Challenge level
    filled star empty star empty star

    Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

  • Fit These Shapes
    problem

    Fit these shapes

    Age
    5 to 11
    Challenge level
    filled star empty star empty star
    What is the largest number of circles we can fit into the frame without them overlapping? How do you know? What will happen if you try the other shapes?
  • A little light thinking
    problem

    A little light thinking

    Age
    14 to 16
    Challenge level
    filled star empty star empty star

    Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?

  • Four Coloured Lights
    problem

    Four coloured lights

    Age
    11 to 14
    Challenge level
    filled star filled star empty star
    Imagine a machine with four coloured lights which respond to different rules. Can you find the smallest possible number which will make all four colours light up?
  • Shapely Lines
    problem

    Shapely lines

    Age
    5 to 7
    Challenge level
    filled star empty star empty star

    This challenge invites you to create your own picture using just straight lines. Can you identify shapes with the same number of sides and decorate them in the same way?

  • Our Numbers
    problem

    Our numbers

    Age
    5 to 7
    Challenge level
    filled star empty star empty star

    These spinners will give you the tens and unit digits of a number. Can you choose sets of numbers to collect so that you spin six numbers belonging to your sets in as few spins as possible?

  • problem

    Counting cogs

    Age
    7 to 14
    Challenge level
    filled star filled star empty star

    Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?

  • I Like ...
    problem

    I like ...

    Age
    5 to 7
    Challenge level
    filled star empty star empty star
    Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?