The $5$ by $5$ tablecloths below each satisfy a different symmetry rule.
 Monday's $5$ by $5$ tablecloth has just $1$ line of symmetry.    Use this interactivity to design tablecloths of other sizes with just $1$ line of symmetry.   Can you find a way of working out how many colours would be needed for an n by n tablecloth (where n is odd)? Tuesday's $5$ by $5$ tablecloth has rotational symmetry of order $4$, and no lines of symmetry.     Use this interactivity to design tablecloths of other sizes with rotational symmetry of order $4$, and no lines of symmetry.   Can you find a way of working out how many colours would be needed for an n by n tablecloth (where n is odd)? Wednesday's $5$ by $5$ tablecloth has $2$ lines of symmetry (horizontal and vertical), and rotational symmetry of order $2$.     Use this interactivity to design tablecloths of other sizes with $2$ lines of symmetry, and rotational symmetry of order $2$.   Can you find a way of working out how many colours would be needed for an n by n tablecloth (where n is odd)? Thursday's $5$ by $5$ tablecloth has $2$ (diagonal) lines of symmetry and rotational symmetry of order $2$.     Use this interactivity to design tablecloths of other sizes with $2$ (diagonal) lines of symmetry and rotational symmetry of order $2$.   Can you find a way of working out how many colours would be needed for an n by n tablecloth (where n is odd)? Friday's $5$ by $5$ tablecloth has $4$ lines of symmetry and rotational symmetry of order $4$.    Use this interactivity to design tablecloths of other sizes with $4$ lines of symmetry and rotational symmetry of order $4$.   Can you find a way of working out how many colours would be needed for an n by n tablecloth (where n is odd)?
At weekends Charlie likes to use tablecloths with an even number of squares. Investigate the number of colours that are needed for different types of symmetric $n$ by $n$ tablecloths where $n$ is even. You may wish to investigate using this interactivity.