What can you see in this diagram?
Could you draw it? Could you draw a similar diagram with just 5 or 6 points around the outside? Try it?

How many lines are there in your diagrams? How many lines are there in the original diagram? Can you find a way of working out the number of lines without counting them? Can you explain your method?

MYSTIC ROSE GAME  Draw a Mystic Rose with 6 points and label them A to F. Players take turns to colour an uncoloured line joining two of the six points A, B, C,… so that it avoids the creation of a triangle with all its edges in their colour. Only triangles with vertices at three of the points A, B, C, D, E and F are included, intersection points are not relevant. Players must colour a line when it is their turn. The loser is the player who completes one of the forbidden triangles, either by mistake or because there is no other move to make.

The game can be played on the phone. Players tell each other which line they are colouring by naming the line AB or AC… etc. Played blindfold, it is good training in concentration, visualization and memory.

Click here for a template of circles so you can draw lines and investigate these patterns.