Visualising and representing

  • Small pepper seedlings in turquoise pots.
    problem

    Painted Purple

    Age
    14 to 16
    Challenge level

    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?

  • Small pepper seedlings in turquoise pots.
    problem

    Facial Sums

    Age
    14 to 16
    Challenge level

    Can you make the numbers around each face of this solid add up to the same total?

  • Small pepper seedlings in turquoise pots.
    problem

    Folding in Half

    Age
    14 to 16
    Challenge level

    How does the perimeter change when we fold this isosceles triangle in half?

  • Small pepper seedlings in orange pots.
    problem

    Packing Boxes

    Age
    14 to 16
    Challenge level

    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.

  • Small pepper seedlings in orange pots.
    problem

    Newspaper Sheets

    Age
    14 to 16
    Challenge level

    From only the page numbers on one sheet of newspaper, can you work out how many sheets there are altogether?

  • Small pepper seedlings in turquoise pots.
    problem

    Bike Shop

    Age
    14 to 16
    Challenge level

    If I walk to the bike shop, but then cycle back, what is my average speed?

  • Small tomato seedlings in pink pots.
    problem

    Relative Time

    Age
    14 to 16
    Challenge level

    Albert Einstein is experimenting with two unusual clocks. At what time do they next agree?

  • Small pepper seedlings in turquoise pots.
    problem

    Pyramidal N-Gon

    Age
    14 to 16
    Challenge level

    The base of a pyramid has n edges. What is the difference between the number of edges the pyramid has and the number of faces the pyramid has?

  • Small pepper seedlings in turquoise pots.
    problem

    Trisected Triangle

    Age
    14 to 16
    Challenge level

    Weekly Problem 34 - 2015
    Four tiles are given. For which of them can three be placed together to form an equilateral triangle?

  • Small pepper seedlings in turquoise pots.
    problem

    Travelling by Train

    Age
    14 to 16
    Challenge level

    Stephen stops at Darlington on his way to Durham. At what time does he arrive at Durham?

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