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## Coin on a Chessboard

Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.

 Puzzle ID: #5328 Fun: (2.39) Difficulty: (2.63) Category: Probability Submitted By: cathalmccabe Corrected By: cnmne

If a chessboard is the size of 80cm, and you throw a coin onto it of diameter 2cm. The centre of the coin falls somewhere within the 64 squares. What is the probability that it lands fully on a white square?

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 dsquared Jul 18, 2002 Good one... once I got over the thought that it may have been a riddle - heh, good thing these categories. Once I knew it was mathematical, it fell into place. sackonto Oct 23, 2002 Not to be too picky, but that would be true only if the puzzle stated, "The ENTIRE coin falls within one of the 64 squares." The puzzle currently says the "CENTER" of the coin will land within one of the 64 squares. This means that the coin can land anywhere on the board except for the center of it landing exactly on a line. Cool teaser though - sorry I had to get critical. Bender Nov 08, 2002 Incorrect, sack. If the question stated that the entire coin landed in one of the 64 squares, the answer would obviously be 1/2, since half the squares are white. It is important in this teaser that the coin's center can land anywhere on the board with equal probability. SPRITEBABE44 Dec 28, 2002 this will sound wrong and dirrty but i agree with bender! + isn't there a simpler explanation! jimbo Mar 14, 2003 Another good one from cath. Well thought out and the conditions were clear and precise. I liked it! mosca Aug 15, 2007 The question seemed to be a bit ambiguous, making it uncertain if the board was 80 centimeters squared or 80 centimeters on a side. If it is 80 centimeters on a side, each square would be 10 cm (about 4 inches) square, rather a huge chessboard, I would think. Interesting teaser though. colin-java Jul 09, 2009 That was fun, did it in about 60 seconds, I posed a similar problem a long time ago on here with a square of side 100 cm, fully containing 2 smaller squares each of side 17 cm. The question was to find the probablity they touch or overlap, I had a nice solution using triangles opqpop Oct 15, 2010 My eyes are bleeding from seeing 32/100 instead of 4/25!!! opqpop Oct 15, 2010 I mean 8/25 X_X