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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 ?

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

\[\text{Thanks !}\]

Note by Sandeep Bhardwaj
2 years, 1 month ago

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Suneet Bendre · 2 years, 1 month ago

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@Suneet Bendre Good job! Can you do it some other way, if possible ? Sandeep Bhardwaj · 2 years, 1 month ago

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@Sandeep Bhardwaj 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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Suneet Bendre · 2 years, 1 month ago

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

Source Sravanth Chebrolu · 2 years, 1 month ago

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@Sravanth Chebrolu HAHAHA...But the lines don't pass through the centers of all the black circles. :P Sandeep Bhardwaj · 2 years, 1 month ago

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@Sandeep Bhardwaj 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 · 2 years, 1 month ago

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can we make the lines by repeating dots more than a one Gauransh Gupta · 2 years ago

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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 Tanishq Varshney · 2 years, 1 month ago

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@Tanishq Varshney It would look better, if you can add a pic of it. Sandeep Bhardwaj · 2 years, 1 month 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 · 2 years, 1 month ago

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@Michael Mendrin 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 · 2 years, 1 month ago

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@Sandeep Bhardwaj 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 · 2 years, 1 month 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 · 2 years, 1 month 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 · 2 years, 1 month ago

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