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# 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
1 year, 4 months ago

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· 1 year, 4 months ago

Good job! Can you do it some other way, if possible ? · 1 year, 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 :))

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· 1 year, 4 months ago

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

Source · 1 year, 4 months ago

HAHAHA...But the lines don't pass through the centers of all the black circles. :P · 1 year, 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 · 1 year, 4 months ago

can we make the lines by repeating dots more than a one · 1 year, 3 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 · 1 year, 4 months ago

It would look better, if you can add a pic of it. · 1 year, 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? · 1 year, 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 ? · 1 year, 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. · 1 year, 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 ? · 1 year, 4 months ago