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Merry Go Round Painting

Topic:
Area, Circle
Dan Anderson pointed out this great puzzler from Tom and Ray Magliozzi, or Click and Clack, the Tappit Brothers from Car Talk. Original puzzle page: http://www.cartalk.com/content/painting-carousel-0 The problem is on the first slide, an exploration on the second and a diagram of the Merry Go Round in the puzzle on the last.