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Coin Dropped on a Chessboard

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

 

Puzzle ID:#43993
Fun:*** (2.27)
Difficulty:*** (3.02)
Category:Probability
Submitted By:javaguru*us**

 

 

 



A table has a chessboard integrated into the center of the table. A round coin fits exactly inside of a square on a chessboard. The coin is dropped on the table and lands face-down, with at least part of the coin on the chessboard.

What is the probability that the coin covers the corner of four chessboard squares?




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Comments

bradon182001*us*
May 02, 2009

Wish I could say I figured it out. Had fun working on it, but I didn't get the answer.Thanks for posting.
gnarldroot
Feb 04, 2010

too easy
zembobo*us*
Jul 07, 2010

"this describes a 9 x 9 square with rounded corners". A square with rounded corners? What kind of square is that? Are you saying in the answer that the table is round? Maybe you should have put that in the question. Exact dimensions would have been nice. I pictured a 9X9 table with a 9x9 chessboard on it. The only way the coin will NOT cover at least 4 corners is if it happens to land exactly in the center of one of the squares (infinitesimal chance of that), or off the table by less than it's radius (any more and it would fall off). So we have two areas we're looking at. 81 for the large table, and 9.25 for the small amount which the coin is allowed to be off the table (9.5^2 - 9^2). The chances in this scenario is 100-[(9.25/81)*100] which is 88.58% chance that the coin will cover the corners of 4 squares.
zembobo*us*
Jul 07, 2010

Wow. Never mind all. My calculations are way off. I wish you could delete posts from here. I believe the answer as posted is correct. I get what he says now about round corners.
krishnanAin*
Aug 22, 2010

Fun, tricky puzzle. I missed out on the rounded corner part and so my answer was slightly off.
abharath27in
May 11, 2013

Problem statement is not very clear.
eighsseAus*
Jul 26, 2013

Very good brain teaser, I should have gotten it correct but I forgot you said the corner of FOUR squares. Instead, I was thinking of every line junction including edges (of which there are 81, not 49)...so I got about 78%. Whoops!
cms271828
Jun 07, 2014

Great puzzle, I got it first time.
Its fairly similar to the puzzle I posted about the square with 2 squares inside that overlap.
I like this type of probability puzzle.



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