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Pink and White

Age 14 to 16 Short Challenge Level:
pink square with adjacent white square

A square of side 8cm, is painted pink and fixed to a table.

An identical square, painted white, is placed on the table alongside the pink square, and has a point P marked one quarter of the way along the diagonal as shown.

If the white square slides once around the pink square, keeping the same orientation and always remaining in contact with the pink square, through what distance does P move?


If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.  

This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.