Knowledge You Can Build On — Est. 1998
Friday Puzzler -- Connect the Dots
Alex Y
The illustration below shows a layout of 9 dots. Your challenge is to connect them with as few connecting straight line segments as possible.
For instance, you could connect them with five line segments as shown below:
Can you connect all 9 dots with only four line segments?
Can you do it with three?
Re: Friday Puzzler -- Connect the Dots
Henry Higginbotham
Does the three-line answer involve any sort of spherical trickernometry?
Re: Friday Puzzler -- Connect the Dots
John Veerkamp
think outside the box
Intriguing idea
Alex Y
The solution I have seen does not involve non-Euclidean geometry, but if you think of a solution using that, post it!
Re: Friday Puzzler -- Connect the Dots
Alex Y
Yes, and the solution for four lines may have inspired the "think outside the box"; it is the most common example given.
Re: Intriguing idea
Henry Higginbotham
Nah, above my pay grade. I was just thinking that if the points existed on the surface of a sphere, lines through the first, second, and third columns would meet at some point. But I guess that would be arcs, anyway, not lines. So I got nothing.
Another "cheat"
Henry Higginbotham
Are these, in fact, dots as opposed to points?
Good Solution
Alex Y
Not the one I was aware of, but that works. You may call those lines "arcs", but that is only from your Euclidean perspective. In fact, they are lines that, because of the spherical failure of the parallel postulate do indeed meet.
Nice solution!
Correct!
Alex Y
Way to go! Two nice "outside the box" solutions to the three-line solution! This is the one I was aware of, but the spherical space is a pretty neat one.
Re: Friday Puzzler -- Connect the Dots
Mark Mandell - Gone Round In New Jersey
How about a single line?
If they are points on a single plane, viewing the plane edge-on and drawing 1 line between the 3 at the edge joins them all since they are all connected by the plane.
ymmv 
