Possess the capability to think out of the box

Can you connect the above 99 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 ?

If you'll upload the image, it will add starts to your response.

Thanks !\text{Thanks !}

Note by Sandeep Bhardwaj
4 years, 4 months ago

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1 vote

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Join Dots Join Dots

Suneet Bendre - 4 years, 4 months ago

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

Sandeep Bhardwaj - 4 years, 4 months ago

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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 Join Dot Logic

Suneet Bendre - 4 years, 4 months ago

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

Source

Sravanth Chebrolu - 4 years, 4 months ago

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

Sandeep Bhardwaj - 4 years, 4 months ago

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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

Sravanth Chebrolu - 4 years, 4 months ago

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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?

Michael Mendrin - 4 years, 4 months ago

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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 ?

Sandeep Bhardwaj - 4 years, 4 months ago

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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.

Michael Mendrin - 4 years, 4 months ago

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@Michael Mendrin 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 ?

Sandeep Bhardwaj - 4 years, 4 months ago

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@Sandeep Bhardwaj 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.

Michael Mendrin - 4 years, 4 months ago

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Consider the dots as matrix , just naming purpose.

connect a11,a22,a33a_{11},a_{22},a_{33}

from a11a_{11} join it with a12,a13a_{12},a_{13} produce it to point PP outside, this is our second straight line

From PP join it with a23,a32a_{23},a_{32}, produce to any point QQ, third line

from QQ join it with a31,a21,a11a_{31},a_{21},a_{11} , this our final fourth line

Tanishq Varshney - 4 years, 4 months ago

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

Sandeep Bhardwaj - 4 years, 4 months ago

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

Gauransh Gupta - 4 years, 3 months ago

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