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.
This discussion board is a place to discuss our Daily Challenges and the math and science
related to those challenges. Explanations are more than just a solution — they should
explain the steps and thinking strategies that you used to obtain the solution. Comments
should further the discussion of math and science.
When posting on Brilliant:
Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.
Markdown
Appears as
*italics* or _italics_
italics
**bold** or __bold__
bold
- bulleted - list
bulleted
list
1. numbered 2. list
numbered
list
Note: you must add a full line of space before and after lists for them to show up correctly
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 :))
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?
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 ?
...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
–
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
–
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.
Easy Math Editor
This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.
When posting on Brilliant:
*italics*
or_italics_
**bold**
or__bold__
paragraph 1
paragraph 2
[example link](https://brilliant.org)
> This is a quote
\(
...\)
or\[
...\]
to ensure proper formatting.2 \times 3
2^{34}
a_{i-1}
\frac{2}{3}
\sqrt{2}
\sum_{i=1}^3
\sin \theta
\boxed{123}
Comments
Join Dots
Log in to reply
Good job! Can you do it some other way, if possible ?
Log in to reply
Solution in Single Line !!
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
I guess that's the way of doing it sir! @Michael Mendrin
Source
Log in to reply
HAHAHA...But the lines don't pass through the centers of all the black circles. :P
Log in to reply
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
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?
Log in to reply
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 ?
Log in to reply
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.
Log in to reply
Log in to reply
Consider the dots as matrix , just naming purpose.
connect a11,a22,a33
from a11 join it with a12,a13 produce it to point P outside, this is our second straight line
From P join it with a23,a32, produce to any point Q, third line
from Q join it with a31,a21,a11 , this our final fourth line
Log in to reply
It would look better, if you can add a pic of it.
can we make the lines by repeating dots more than a one