Visualising and representing

  • Changing Places
    problem

    Changing Places

    Age
    14 to 16
    Challenge level

    Place a red counter in the top left corner of a 4×4 array, which is covered by 14 other smaller counters, leaving a gap in the bottom right hand corner (HOME). What is the smallest number of moves it will take to move the red counter to HOME?

  • Small pepper seedlings in turquoise pots.
    problem

    Out of the Window

    Age
    14 to 16
    Challenge level

    Find out how many pieces of hardboard of differing sizes can fit through a rectangular window.

  • Triangles within Triangles
    problem

    Triangles Within Triangles

    Age
    14 to 16
    Challenge level

    Can you find a rule which connects consecutive triangular numbers?

  • Small pepper seedlings in turquoise pots.
    problem

    Rectangle Rearrangement

    Age
    14 to 16
    Challenge level

    A 3×8 rectangle is cut into two pieces... then rearranged to form a right-angled triangle. What is the perimeter of the triangle formed?

  • Small pepper seedlings in turquoise pots.
    problem

    Twelve Cubed

    Age
    14 to 16
    Challenge level

    A wooden cube with edges of length 12cm is cut into cubes with edges of length 1cm. What is the total length of the all the edges of these centimetre cubes?

  • Small pepper seedlings in turquoise pots.
    problem

    Dicey Directions

    Age
    14 to 16
    Challenge level

    An ordinary die is placed on a horizontal table with the '1' face facing East... In which direction is the '1' face facing after this sequence of moves?

  • The perforated cube
    problem

    The Perforated Cube

    Age
    14 to 16
    Challenge level

    A cube is made from smaller cubes, 5 by 5 by 5, then some of those cubes are removed. Can you make the specified shapes, and what is the most and least number of cubes required ?

  • Efficient packing
    problem

    Efficient Packing

    Age
    14 to 16
    Challenge level

    How efficiently can you pack together disks?

  • Building Gnomons
    problem

    Building Gnomons

    Age
    14 to 16
    Challenge level
    Build gnomons that are related to the Fibonacci sequence and try to explain why this is possible.
  • Small pepper seedlings in turquoise pots.
    problem

    Eulerian

    Age
    14 to 16
    Challenge level

    Weekly Problem 37 - 2014
    Which of the five diagrams below could be drawn without taking the pen off the page and without drawing along a line already drawn?

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