Answer to the Question 10/03
THREE-SIDED COINThe question was:
What should be the dimensions of a coin that has probability of 1/3 to fall on its obverse ("heads") side, 1/3 - on its reverse ("tails") side, and 1/3 - on its edge.
(1/04) The problem has been solved (1/1/04) by Shiva (e-mail rsiva@uclink.berkeley.edu).
The answer: The width of the coin should be 2R/sqrt(3), where R is the radius of the coin.
The solution: For the probability to be the same, since the coin is round, a vertical line through the center of gravity should pass through a corner when the coin is tilted by 30 degrees from the "standing on the edge" position. This way, out of possible 360 degrees, one third (120 degrees) will correspond to the coin eventually resting on the edge.
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