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Attractive Tablecloths printable worksheet - tablecloths
Attractive Tablecloths printable worksheet - templates


Charlie has been designing square tablecloths for each weekday. He likes to use as many colours as he possibly can but insists that his tablecloths have some symmetry.

 


The $5$ by $5$ tablecloths below each satisfy a different symmetry rule.

 

 


Monday's $5$ by $5$ tablecloth has just $1$ line of symmetry. 
 
Design some square tablecloths of other odd by odd sizes with just $1$ line of symmetry.

Check you agree that a $7$ by $7$ tablecloth can have at most 28 colours.
 
Can you find a way of working out the maximum number of different colours that can be used on an n by n tablecloth (where n is odd), following Monday's rule?
 

 

 




Tuesday's $5$ by $5$ tablecloth has rotational symmetry of order $4$, and no lines of symmetry.  
 
Design some square tablecloths of other odd by odd sizes with rotational symmetry of order $4$, and no lines of symmetry.
 
Check you agree that a $7$ by $7$ tablecloth can have at most 13 colours.
 
Can you find a way of working out the maximum number of different colours that can be used on an n by n tablecloth (where n is odd), following Tuesday's rule?
 


 

 




Wednesday's $5$ by $5$ tablecloth has $2$ lines of symmetry (horizontal and vertical), and rotational symmetry of order $2$.  
 
Design some square tablecloths of other odd by odd sizes with $2$ lines of symmetry, and rotational symmetry of order $2$.
 
Check you agree that a $7$ by $7$ tablecloth can have at most 16 colours.
 
Can you find a way of working out the maximum number of different colours that can be used on an n by n tablecloth (where n is odd), following Wednesday's rule?

 

 

 




 
Thursday's $5$ by $5$ tablecloth has $2$ (diagonal) lines of symmetry and rotational symmetry of order $2$.  
 
Design some square tablecloths of other odd by odd sizes with $2$ (diagonal) lines of symmetry and rotational symmetry of order $2$.
 
Check you agree that a $7$ by $7$ tablecloth can have at most 16 colours.
 
Can you find a way of working out the maximum number of different colours that can be used on an n by n tablecloth (where n is odd), following Thursday's rule?

 


 

 

 


 
Friday's $5$ by $5$ tablecloth has $4$ lines of symmetry and rotational symmetry of order $4$. 
 
Design some square tablecloths of other odd by odd sizes with $4$ lines of symmetry and rotational symmetry of order $4$.
 
Check you agree that a $7$ by $7$ tablecloth can have at most 10 colours.
 
Can you find a way of working out the maximum number of different colours that can be used on an n by n tablecloth (where n is odd), following Friday's rule?

 

EXTENSION
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.