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Sorting Symmetries

Age 7 to 11 Challenge Level:

Many of you wrote to tell us that there were six ways of posting the triangle into the shape sorter. JC explained:


There are six ways to put the triangle into the hole. On the blue side, you can have the dot in the top angle, the bottom left or bottom right angle. It is the same on the flip, yellow, side!


Mike tackled the second part of the problem (using the diagrams below):

six symmetries


I will call these six symmetries A, B, C (along the top row) and D, E, F (along the bottom row).

If you turn triangle A 120 degrees clockwise you get to position B. If you then flip it vertically you go from B to F.

If you turn triangle A 120 degrees anticlockwise you get to position C. If you then flip the triangle you get to position E.

Philippa also noticed that you can do a whole turn before flipping:

If you turn triangle A 360 degrees clockwise or anticlockwise you get back to position A. If you then flip it you get to position D.

Well done everyone!