Connect Nine DotsDate: 11/4/96 at 14:8:42 From: gil sela Subject: Re: Drawing problem I saw a very beautiful problem but I couldn't solve it. It looked simple but after a second, I gave up: Draw 4 lines connecting the 9 dots without lifting the pen x x x x x x x x x Date: 12/04/96 at 15:18:07 From: Doctor Keith Subject: Re: Drawing problem It is a nice problem. Allow me to first give you a piece of advice and a picture instead of the answer. You can then try it again and see if you can get it on your own. If you get stuck then, the solution is below my suggestion. My advice is to remember that you are not stuck with the nine dots as corners. This means you can continue the line outside the dots and then turn. So consider this diagram with two extra dots, which I claim can be done with the same 4 lines without lifting the pen. Try drawing lines that include these points as corners and see what you get. X x x x x x x X x x x To see the solution on the Web, take a look at this page: http://mathforum.org/k12/k12puzzles/join.dots.html If you enjoy problems like this you might want to consider a book on graph theory or classic math problems, or look at more of our line puzzles (at the above URL). Good luck! -Doctor Keith, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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