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Take it in turns to add a band to the board to make any of the shapes you are allowing.
A band can share a peg with other bands, but the shapes must not overlap (except along the edges and pegs).
A player loses when they cannot make a shape on their turn.
For your choice of shapes, how does the winning strategy change as you increase the number of pegs on the board?
If you keep the number of pegs fixed, how does the winning strategy alter as you change the shapes you are permitted to make?
How is the game affected if you play to lose?
Perhaps you can invent some of your own games using the pegboard? Email us if you'd like to share your ideas.