# Possess the capability to think out of the box

Can you connect the above $9$ dots with just 4 straight lines which can be drawn without lifting the pencil off the paper? If yes, then how ? If no, then why ?

$\text{Thanks !}$

Note by Sandeep Bhardwaj
4 years, 4 months ago

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Join Dots

- 4 years, 4 months ago

Good job! Can you do it some other way, if possible ?

- 4 years, 4 months ago

Solution in Single Line !!

   Given condition : 'drawn without lifting the pencil off the paper'
Assumption : Paper can be folded in zig zag manner.


Step 1. : Draw 9 dots (3x3) on 'post it paper'
Step 2 : Fold paper in Zip Zag manner in such a way that all 9 Dots are on the top edge (See image)
Step 3: Join all three mountain edge side paper together.
Step 4: Draw a line with Pencil (thick nib pencil ) on those dots.
Step 5: Straighten the paper (You are done :))

Join Dot Logic

- 4 years, 4 months ago

I guess that's the way of doing it sir! @Michael Mendrin

- 4 years, 4 months ago

HAHAHA...But the lines don't pass through the centers of all the black circles. :P

- 4 years, 4 months ago

Yes, that the only problem sir. But as Michael sir, had said that the dots are considered as having non-zero diameters. . . I submitted this. :P

- 4 years, 4 months ago

I can actually do it with 3 straight lines without lifting the pencil off the paper, because the white dots have non-zero diameters. But can it be done with 4, if the white dots are white points instead?

- 4 years, 4 months ago

Sir, can you add a pic of how will you do it with 3 straight lines without lifting the pencil off the paper, and will your lines pass through the center of every white dot with non-zero diameter ?

- 4 years, 4 months ago

Sandeep, here's the graphic

...but I did this because I just sat down here with my coffee and didn't see what Sravanth hath already wrought. I must admit, his is the nicer picture.

- 4 years, 4 months ago

Sir, can you help me out with graph plotter ? I mean how do you sketch the graphs, your graphical stuffs are always amazing, What software do you use ?

- 4 years, 4 months ago

My old tried-and-true mathematica, which I've been using for quite some time now in my past work. It has its good points and bad points. Not necessarily the best graphing software. I used to do computer graphics and animations, which allowed me to do things this old mathematica simply cannot do.

- 4 years, 4 months ago

Consider the dots as matrix , just naming purpose.

connect $a_{11},a_{22},a_{33}$

from $a_{11}$ join it with $a_{12},a_{13}$ produce it to point $P$ outside, this is our second straight line

From $P$ join it with $a_{23},a_{32}$, produce to any point $Q$, third line

from $Q$ join it with $a_{31},a_{21},a_{11}$ , this our final fourth line

- 4 years, 4 months ago

It would look better, if you can add a pic of it.

- 4 years, 4 months ago

can we make the lines by repeating dots more than a one

- 4 years, 3 months ago