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 Chessboard Coin (Posted on 2004-10-08)
I've a chessboard of side 80cm.

You've a coin of diameter 2cm, and you throw it on to the chessboard. The center of the coin falls somewhere on the chessboard.

What is the likelihood that the coin is completely within a white square?

 See The Solution Submitted by SilverKnight Rating: 2.8333 (12 votes)

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 re(3): Dumb Question | Comment 10 of 21 |
(In reply to re(2): Dumb Question by Richard)

If the coin is required to land totally on the board, the numerator stays the same, as that represents the total area where the center can be and have the whole coin on a white square.  The denominator is lowered to represent the reduced effective area of where the coin can land.  The center must then land on a square that is 78 cm x 78 cm, or 6084 cm^2.  The probability is then 2048/6084 = 0.3366206443129520052 or about 33.66%.
 Posted by Charlie on 2004-10-08 14:01:40

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