Square numbers

  • Picture a Pyramid ...
    problem

    Picture a Pyramid

    Age
    7 to 11
    Challenge level

    Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?

  • Seven Square Numbers
    problem

    Seven Square Numbers

    Age
    7 to 11
    Challenge level

    Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.

  • Four Coloured Lights
    problem

    Four Coloured Lights

    Age
    11 to 14
    Challenge level
    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?
  • Small tomato seedlings in pink pots.
    problem

    Square Triangle

    Age
    11 to 14
    Challenge level

    How many triangles have all three angles perfect squares (in degrees)?

  • Square Routes
    problem

    Square Routes

    Age
    11 to 14
    Challenge level

    How many four digit square numbers are composed of even numerals? What four digit square numbers can be reversed and become the square of another number?

  • Smith and Jones
    problem

    Smith and Jones

    Age
    14 to 16
    Challenge level

    Mr Smith and Mr Jones are two maths teachers. By asking questions, the answers to which may be right or wrong, Mr Jones is able to find the number of the house Mr Smith lives in... Or not!

  • Small tomato seedlings in pink pots.
    problem

    Pythagorean Quadruple

    Age
    14 to 16
    Challenge level

    The sum of three square numbers equals $121$. What can those numbers be...

  • Odd Differences
    problem

    Odd Differences

    Age
    14 to 16
    Challenge level

    The diagram illustrates the formula: 1 + 3 + 5 + ... + (2n - 1) = n² Use the diagram to show that any odd number is the difference of two squares.

  • Triangles within Squares
    problem

    Triangles Within Squares

    Age
    14 to 16
    Challenge level

    Can you find a rule which relates triangular numbers to square numbers?

  • Small tomato seedlings in pink pots.
    problem

    Square Sum

    Age
    14 to 16
    Challenge level

    One of these numbers is the largest of nine consecutive positive integers whose sum is a perfect square. Which one is it?

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