Est. 1998 — 27 years of woodworking knowledge
Friday Puzzler -- Chess Board 3 of 3
Alex Y
Well, not actually a chess board, since that is too small. Let's use a room with a floor painted in a chessboard pattern with 1" squares, as an approximation of an infinite chess board.
If you throw a coin, with a diameter of 1/2", on the floor, what is the probability that it will be touching two colors?
Re: Friday Puzzler -- Chess Board 3 of 3
Henry Higginbotham
If the condition is that the coin touches at least one other square besides the one the center of the coin lies on, then:
Area of one square = 1.000
Area of a R0.25 radius circle centered on the coin = 0.1963
(The coin's center must stay within this circle for the coin to stay within one square.)
So the probability would be 1 - 0.1963 = 0.8037.
It seems that would hold for any size board.
If the condition is that it only touch a part of one other square, as opposed to covering a "four corners," I'd have to cipher on that some more.
Right approach
Alex Y
But mistaken parenthetical.
I'm not following your alternative interpretation.
Re: Friday Puzzler -- Chess Board 3 of 3
Ed in Leaside
I think it's 50:50
Re: Right approach
Henry Higginbotham
Trying this again: To stay within one color, the coin's center must remain within a square with 0.5" sides, which would have an area of 0.25. So probability of touching another color = 0.75.
The alternate scenario (which I don't think was the intent) is that the coin touches another color, but only in one other square. In the photo, only the lower right coin satisfies this condition. There are four areas where this could happen, 0.25 x 0.50 each, so that probability would be 0.50.
Correct!
Alex Y
And your solution to the other problem (which you correctly guessed was not the intent) is also correct.
Re: Friday Puzzler -- Chess Board 3 of 3 *LINK*
Larry Barrett
Here is a link to a somewhat similar problem that involves dropping a needle on a floor with equally spaced strips (think typical oak floors). This is a probability problem posed by the Comte de Buffon, and is known as Buffon's Needle. It turns out to be a method to estimate π (pi). Read down a few paragraphs.
Buffon's Needle
Thanks for sharing that. Interesting.
Re: Friday Puzzler -- Chess Board 3 of 3
AlMorgan
Im going to say 75% probable that a 1/2 coin thrown on a chess board made up 1" squares that it will touch 2 colors. That would be because if the coin lands anywhere on the 1/4" border perimeter of the 1" square it will be touch 2 colors...the 1/4 border adds up to .75 square in. Thats my story and I'm sticking to it.