Monday, March 29, 2010
This week's post on Steve Strogatz's New York Times column reminded me of this puzzle. In it he re-explains math in a creative and intuitive way, from basic counting through imaginary numbers, functions, and more. The post reminded me of this because in it he talks about how mathematical functions can explain every-day shapes, such as how water at a drinking fountain forms a parabola. A hanging chain forms a catenary, but its shape can be approximated with a parabola. It is a great new one I found at Wu Riddles, and apparently it originated at a Microsoft Interview. BUT: don't be intimidated by all the math, I have faith that you can solve this one.
You have a 6-foot long chain that is suspended at its ends, tacked to a wall. The tacks are parallel to the floor. Due to gravity, the middle part of the chain hangs down below the ends, forming a 'U'-type shape; the height of this 'U' is 3 feet from top to bottom. Find the distance in between the tacks.
As the commenters pointed out below, the distance between the tacks is zero. The only way for the dip in the chain to be three feet is for the chain to drop 3ft straight down, then 3ft straight up. There is no chain left to spare for horizontal distance.
Posted by Charlie Guthrie at 11:19 AM