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A square piece of wood, of side 8cm, is painted pink and fixed to a table. An equal 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. Whilst keeping the orientation on the table and always remaining in contact with the pink square, the white square now slides once around the pink square.
Through what distance does P move?
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This problem is taken from the UKMT Mathematical Challenges.