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P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?

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A and C are the opposite vertices of a square ABCD, and have coordinates (a,b) and (c,d), respectively. What are the coordinates of the vertices B and D? What is the area of the square?

Changing Places

Age 14 to 16
Challenge Level

Once started on the journey home why is every third move important?

What is special about those counters that don't move?