9 spots

wolfgang59
Posers and Puzzles 23 Mar '09 21:48
1. wolfgang59
Mr. Wolf
23 Mar '09 21:48
Draw nine dots so that they are arranged in a 3x3 square.

Can you connect all nine dots with 4 STRAIGHT lines without taking pen (or pencil or chalk or other marking-tool) from paper?

Is it possible?
2. 23 Mar '09 22:45
Yes. Hint: you only need "queen moves" (moves in the 8 directions).
3. sonhouse
Fast and Curious
24 Mar '09 00:451 edit
Originally posted by wolfgang59
Draw nine dots so that they are arranged in a 3x3 square.

Can you connect all nine dots with 4 STRAIGHT lines without taking pen (or pencil or chalk or other marking-tool) from paper?

Is it possible?
Sho nuff. We got that one in the 8th grade. You just have to think outside the box, so to speak.
4. wolfgang59
Mr. Wolf
24 Mar '09 16:41
Originally posted by sonhouse
Sho nuff. We got that one in the 8th grade. You just have to think outside the box, so to speak.
Kids get it quicker than adults.
5. 24 Mar '09 16:45
I've heard of a way to connect all 9 dots with only 3 lines, believe it or not. This requires thinking even further outside the box though..
6. 24 Mar '09 17:38
Originally posted by geepamoogle
I've heard of a way to connect all 9 dots with only 3 lines, believe it or not. This requires thinking even further outside the box though..
Easy enough if the dots are of finite size, and you've got a very big piece of paper.
7. 24 Mar '09 18:12
Originally posted by wolfgang59
Draw nine dots so that they are arranged in a 3x3 square.

Can you connect all nine dots with 4 STRAIGHT lines without taking pen (or pencil or chalk or other marking-tool) from paper?

Is it possible?
It's not only possible, I can do it in one line, and one stratight line only. Not that difficult. You really have to think outside the box.
8. 24 Mar '09 20:06
Originally posted by FabianFnas
It's not only possible, I can do it in one line, and one stratight line only. Not that difficult. You really have to think outside the box.
one straight line? That's impossible!
9. forkedknight
Defend the Universe
24 Mar '09 21:38
Originally posted by Thomaster
one straight line? That's impossible!
My dots are very small and I'm using a sharpy.
10. 25 Mar '09 00:01
what if the 3x3 square was not made from the nine dots but they were arranged in some other 3x3 square? in fact arrange them on top of each other and cover them with another dot hence 0 lines
11. forkedknight
Defend the Universe
25 Mar '09 00:50
Originally posted by deriver69
what if the 3x3 square was not made from the nine dots but they were arranged in some other 3x3 square? in fact arrange them on top of each other and cover them with another dot hence 0 lines
Because then it wouldn't be a square, nor 3x3...?
12. 25 Mar '09 06:01
Originally posted by Thomaster
one straight line? That's impossible!
Not at all, I can do it with no difficulty.
Everytime I present this solution people say "You're cheating!" but I'm not. What they really mean is "You don't do it as it is meant to do!" or "We didn't think of that!".
So there is definitely a solution for 9 dots and one straight line.
13. wolfgang59
Mr. Wolf
25 Mar '09 12:41
maybe I should have said 9 points rather than dots? and defined point, and line and straight.

In fact I never really defined "9" did I?
14. 25 Mar '09 13:001 edit
Originally posted by wolfgang59
maybe I should have said 9 points rather than dots? and defined point, and line and straight.

In fact I never really defined "9" did I?
Well, you can always narrow the definition to the extent that only one solution is possible. But the problem stated as it was from the beginning, in lay terms.

Put the nine points slighle tilted, roll the paper to a cylindre, and then draw the line around the cylender, hitting three points every turn.

That's *one* solution, but I assumed that the paper should be finite in size and flat. So my solution is 9 points on a flat paper. You can use a ruler to make the line perfectly straight.

Why use four lines when one is enough?
15. 25 Mar '09 14:12
Originally posted by FabianFnas
Well, you can always narrow the definition to the extent that only one solution is possible. But the problem stated as it was from the beginning, in lay terms.

Put the nine points slighle tilted, roll the paper to a cylindre, and then draw the line around the cylender, hitting three points every turn.

That's *one* solution, but I assumed that the pa ...[text shortened]... can use a ruler to make the line perfectly straight.

Why use four lines when one is enough?
Your cilinder trick doesn't work, since the line should remain straight. (what is impoosible on a rolled paper)

I think I understand how you do it with one line. You take two papers.
First you hit three dots with a straight line and you 'park' the line in the second paper. You can simply move the dots :-)