Visualising and representing

  • Making Tracks
    problem

    Making Tracks

    Age
    14 to 16
    Challenge level
    filled star filled star empty star
    A bicycle passes along a path and leaves some tracks. Is it possible to say which track was made by the front wheel and which by the back wheel?
  • Semaphore
    problem

    Semaphore

    Age
    11 to 14
    Challenge level
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    I am standing behind five pupils who are signalling a five-digit number to someone on the opposite side of the playground. What number is actually being signalled?
  • Painted Purple
    problem

    Painted Purple

    Age
    14 to 16
    Challenge level
    filled star filled star empty star
    Three faces of a $3 \times 3$ cube are painted red, and the other three are painted blue. How many of the 27 smaller cubes have at least one red and at least one blue face?
  • Don't Be Late
    problem

    Don't Be Late

    Age
    11 to 14
    Challenge level
    filled star filled star empty star
    Mary is driving to Birmingham Airport. Using her average speed for the entire journey, find how long her journey took.
  • Facial Sums
    problem

    Facial Sums

    Age
    14 to 16
    Challenge level
    filled star filled star empty star
    Can you make the numbers around each face of this solid add up to the same total?
  • Adjacent Factors
    problem

    Adjacent Factors

    Age
    11 to 14
    Challenge level
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    Two numbers can be placed adjacent if one of them divides the other. Using only $1,...,10$, can you write the longest such list?
  • Folding in Half
    problem

    Folding in Half

    Age
    14 to 16
    Challenge level
    filled star filled star empty star
    How does the perimeter change when we fold this isosceles triangle in half?
  • Reading from Behind
    problem

    Reading From Behind

    Age
    11 to 14
    Challenge level
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    Can you find the time between 3 o'clock and 10 o'clock when my digital clock looks the same from both the front and back?
  • Packing Boxes
    problem

    Packing Boxes

    Age
    14 to 16
    Challenge level
    filled star filled star empty star
    Look at the times that Harry, Christine and Betty take to pack boxes when working in pairs, to find how fast Christine can pack boxes by herself.
  • Newspaper Sheets
    problem

    Newspaper Sheets

    Age
    14 to 16
    Challenge level
    filled star filled star empty star
    From only the page numbers on one sheet of newspaper, can you work out how many sheets there are altogether?