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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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 solution | Comment 4 of 21 |

The coin has a radius of 1 cm. Each square has a side equal to 80/8 = 10 cm.  So the center of the circle has to be at least 1 cm from the edge within a white square, making the good area within each white square 8*8=64 cm^2.

There are 32 white squares on the chessboard, making the total good area 64*32=2048 cm^2.  The whole chessboard is 80*80=6400 cm^2.

2048/6400 = 8/25 = .32, for a 32% probability.

 Posted by Charlie on 2004-10-08 09:29:35

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