Join the DotsDate: 09/02/2001 at 21:34:39 From: Christi Subject: Geometry If you have 9 dots, like this: . . . . . . . . . how can you connect them with only 4 lines without picking up your pencil or going through a dot more than once? Please help. Date: 09/06/2001 at 08:36:33 From: Doctor Ann Subject: Re: Geometry Hi Christi, This question brings back happy memories for me because it is the first "brain teaser" that I remember working. It is also a good example of thinking "outside the box." For clarity, I am going to number the dots: 1 2 3 4 5 6 7 8 9 Start at point 4. Draw the first line from point 4 and through point 7. However, (here's the trick), DRAW THE LINE BEYOND POINT 7 AND INTO THE SPACE JUST BELOW THE 7. The second line is drawn from the space below the 7, and through points 8 and 6. Again, don't end the line segment at 8. Continue the line outward (northeast) until it is just to the right of point 3, then stop. Line Three starts at that point, then goes (left) through points 2 and 1, then stops AT 1. The last line connects 1 with 9 (through 5). For an illustration, see: http://mathforum.org/k12/k12puzzles/join.dots.html I hope that is a clear explanation of the problem. If not, or if you have another question, feel free to write again. - Doctor Ann, The Math Forum http://mathforum.org/dr.math/ |
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