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Rolling coins

Posted on: April 27th, 2013 by
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There are 2 puzzles today. The easier puzzle first:
Roll a penny around another fixed penny in the center with edges in close contact. After moving half circle around the center penny, you will find the penny in motion has rotated 360 degrees.
Why?

via CSE blog

Now for the harder puzzle:
Place four $1 coins as shown in the diagram below:

Now roll the shaded coin anti- clockwise around the other three, touching them the entire time, until it returns to the original position. How much has the shaded coin rotated relative to its centre?
via AMS puzzle corner


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