2872 /www/nrich/html/content/id/2872/ 2 2011-02-01T00:00:01 <mdoxml version="1.0"> <p>Before playing this game, you might like to have a go at the simpler version, <a href="http://nrich.maths.org/public/viewer.php?obj_id=2871&amp;part=index">Board Block</a> .<br></br> <a href="/content/id/2872/circleAngles.swf">Full Screen Version</a><br></br> <mdo:flash height="400" width="550"><param name="allowfullscreen" value="true" ></param><param name="movie" value="/content/id/2872/circleAngles.swf" ></param><param name="flashplayerversion" value="7" ></param></mdo:flash><br></br> This version is also for two players and can be played on the interactive version of the pegboard, or a real circular pegboard if you have one.<br></br> <br></br> Firstly, choose the number of pegs on your board.<br></br> Decide what shapes you will be allowed to make.<br></br> You could allow:</p> <ul> <li>triangles and quadrilaterals</li> </ul> <ul> <li>triangles, quadrilaterals and pentagons</li> </ul> <ul> <li>triangles, quadrilateral, pentagons and hexagons</li> </ul> <ul> <li>triangles, quadrilaterals, pentagons, hexagons and...</li> </ul> <p>Take it in turns to add a band to the board to make any of the shapes you are allowing.<br></br> A band can share a peg with other bands, but the shapes must not overlap (except along the edges and pegs).<br></br> A player loses when they cannot make a shape on their turn.<br></br> <br></br> For your choice of shapes, how does the winning strategy change as you increase the number of pegs on the board?<br></br> <br></br> If you keep the number of pegs fixed, how does the winning strategy alter as you change the shapes you are permitted to make?<br></br> <br></br> How is the game affected if you play to lose?<br></br> <br></br> Perhaps you can invent some of your own games using the pegboard? <a href="mailto:nrich@maths.cam.ac.uk">Email</a> us if you&#39;d like to share your ideas.<br></br>  </p> </mdoxml> 2 5 0 1 0 0 0 Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent? Using, Applying and Reasoning about Mathematics Games 2D Geometry, Shape and Space Other polygons Mathematics Tools Pinboard/geoboard Information and Communications Technology Interactivities