- 29 Jan '06 10:40 / 3 editscover up the bottom of this post if you want to slove this

try to solve this ,here are the rules you must connect all the numbers.

you may draw a total of 4 lines.lines must be straight,and you maynot retrace or go back on a line.you may cross lines.

...1....2....3

...4....5....6

...7....8....9

the solution...think outside the box.add points A and B

..................B

......1....2....3

......4....5....6

A....7....8....9

the solution is 15987A42B369 - 30 Jan '06 09:55Given that the numbers are not just points, you can do this with only 3 lines.

.....................1....2....3

........................................................A

.....................4....5....6

B..................

.....................7....8....9

You start at the very top of the number 1, go through the middle of the 2 and clip the base of the 3 and head off in the direction of A (A probably needs to be further to the right, but it gives you the general idea). This first line slopes down to the right.

Next you slope down to the left going through the top of the 6, middle of 5 and base of 4 towards B. Finally hit the top of 7, middle of 8 and base of 9.

*Originally posted by aspviper666***...think outside the box**

Like it! - 30 Jan '06 21:21 / 1 edit

From the original post i.e. rules*Originally posted by Diapason***Given that the numbers are not just points, you can do this with only 3 lines.**

.....................1....2....3

........................................................A

.....................4....5....6

B..................

.....................7....8....9

You start at the very top of the number 1, go through the middle of the 2 and clip the base o ...[text shortened]... base of 9.

*Originally posted by aspviper666*

[b]...think outside the box

Like it![/b]

lines must be straight - 30 Jan '06 21:51

The lines in my solution*Originally posted by aspviper666***From the original post i.e. rules**

lines must be straight**are**straight ... just not horizontal.

The first straight line goes diagonally downwards to the right at a very shallow gradient. The second goes downwards to the left at a very shallow gradient and the final one to the right.

This wouldn't work if there were points involved, but does because the numbers have 'height'.

Sorry I didn't explain this clearly the first time. - 31 Jan '06 08:08

Absolutely right.*Originally posted by Diapason***The lines in my solution [b]are**straight ... just not horizontal.

This wouldn't work if there were points involved, but does because the numbers have 'height'.[b]

The problem posed indicated no points, mathematical or otherwise. The problem indicated numbers and those ar not pointlike.

Three straight lines is enough for this problem. - 31 Jan '06 22:07

the numbers are supposed to be points or dots*Originally posted by Diapason***The lines in my solution [b]are**straight ... just not horizontal.

The first straight line goes diagonally downwards to the right at a very shallow gradient. The second goes downwards to the left at a very shallow gradient and the final one to the right.

This wouldn't work if there were points involved, but does because the numbers have 'height'.

Sorry I didn't explain this clearly the first time.[/b]

(see thread title)

I used numbers so i could devise a notation system

to post solutions.

I can see where you got the idea about the height off the numbers.

I am sorry about any confusion.

cheers - 01 Feb '06 08:03This is a very interesting problem if you go beyond the famous original problem.

For example: If you put the points on a non-flat surface, for example a sphere or a torus, is the problem solvable with fewer than four lines? Perhaps only one line, circling?

Or: if you extend the problem, not only 3 by 3 but 4 by 4, how many lines are needed?

Or, further: If you, instead of using a 3 by 3 plane, use a 3 by 3 by 3 cube, how many lines are then needed to connect the dots? Or perhaps planes? - 03 Feb '06 11:55

Yes a friend of mine proposed a solution involving a line encirling the world.I guess thats a way to solve it and definitely out side the box.*Originally posted by FabianFnas***This is a very interesting problem if you go beyond the famous original problem.**

For example: If you put the points on a non-flat surface, for example a sphere or a torus, is the problem solvable with fewer than four lines? Perhaps only one line, circling?

Or: if you extend the problem, not only 3 by 3 but 4 by 4, how many lines are needed?

Or, f ...[text shortened]... , use a 3 by 3 by 3 cube, how many lines are then needed to connect the dots? Or perhaps planes?

Good points and thoughts by all.

I am not a math dude myself.

thanks