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'Peg Rotation' printed from http://nrich.maths.org/

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Here we have a kind of peg board. The holes go all the way through so the pegs may be seen from the top or underneath.

sq1

You'll see the 4 blue pegs.
Now the peg board is either:
  • flipped over - north to south, OR east to west, OR north-east to south-west, OR north-west to south-east;
  • or it is rotated clockwise or anticlockwise.

Can you find out which movements could produce the four next views?
 
sq3sq4
sq5sq2

You could make some of your own and get your friends to see if they can find how you've moved it to make your next picture.
Try now to put 4 pegs in so that when you do a move with the board it still looks the same.

Now I've made a triangular board to do the same things.
Here's the starting view:
 
Tri1

How has it been moved to show these views?
Tri2
Tri3

Hope you've had fun exploring these.
Can you think up ways of changing what I've done so that you can explore further?