Squares

  • Eight hidden squares
    problem

    Eight hidden squares

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

    On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?

  • Ten Hidden Squares
    problem

    Ten hidden squares

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

    These points all mark the vertices (corners) of ten hidden squares. Can you find the 10 hidden squares?

  • Baravelle
    problem

    Baravelle

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

    What can you see? What do you notice? What questions can you ask?

  • Coloured Edges
    problem

    Coloured edges

    Age
    11 to 14
    Challenge level
    filled star empty star empty star
    The whole set of tiles is used to make a square. This has a green and blue border. There are no green or blue tiles anywhere in the square except on this border. How many tiles are there in the set?
  • Tilted Squares
    problem

    Tilted squares

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

    It's easy to work out the areas of most squares that we meet, but what if they were tilted?

  • Hidden Squares
    problem

    Hidden squares

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

    Can you find the squares hidden on these coordinate grids?

  • On the Edge
    problem

    On the edge

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

    If you move the tiles around, can you make squares with different coloured edges?

  • Square coordinates
    problem

    Square coordinates

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

    A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?

  • Squares in rectangles
    problem

    Squares in rectangles

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

    A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What sizes of rectangle contain exactly 100 squares? Can you find them all?