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Puzzle 113.  COUNTERFEIT COIN

You have 25 gold coins.  One on these coins is lighter, while the rest of the coins have the same weight.  If you have a balance, how would you determine which coin is the lighter one with 3 weighings. 

 

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Bits and Beyond...

PI

Pi is the ratio of the circumference of a circle to its diameter.  The approximation of pi has began as early as the ancient times.  One of the well-known one was by the great Greek mathematician Archimedes, who started approximating Pi by inscribing a hexagon into a circle.  With the hexagon, pi was calculated to have a value of 3.  Doubling the number of sides and inscribing a dodecagon in the same circle, his new value became closer to pi.  He continued until he used a 96-gon, and found a better approximation of 3.1419.  A similar method was used by the Chinese mathematician Lui Hui.  He used a 3,072-gon and acquired a value of 3.1416, a very good approximation approximation.

 

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