Maria has three red coins and one blue coin, all with the same radius and with a rubbery edge. She places the three red coins on the table at the vertices of an equilateral triangle so that they touch each other in pairs, then she also places the blue one on the table so that it touches one of the red coins. Now, keeping the red coins fixed, she rolls the blue one so that it always remains adherent to at least one of the red coins and the rubbery edges do not slip. After a complete circuit around the group of the three red coins, the blue coin returns to the starting point; how many turns has it made on itself?
Pick one
Solution
Solution:
The answer is (A). Since we must make a complete circuit, we may assume we start at a point where the blue coin touches 2 red coins at the same time. In the path that the blue coin now makes while adhering to one of the two, its center travels a semicircle; but meanwhile the edge in turn performs a rotation of 180∘ about the center, so the coin makes a complete turn. Since this repeats 3 times, in total the coin makes 3 turns on itself which end exactly when it has finished the path returning to the starting point.
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Source: MathNet,
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