Think Outside The Box Sometimes

Logic Level 2

Using only straight lines, what is the least number of lines needed to cover all 9 spots if you were using a pen and it could not be removed from the page?

Treat the spots as a 0-dimensional object. They do not have length or width.


The answer is 4.

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18 solutions

if we're bending the rules then all dots can be connected by one very thick line

Michael Wolf - 6 years, 3 months ago

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Agree! my final answer was 1 line, because of the hint "think out of the box" :)

Marco Luca Sbodio - 6 years, 3 months ago

I said 4 because 3 an 5 didnt work 😂😂😂😂😂😂😂

Mayur Chauhan - 5 years, 5 months ago

Maybe even a single point

Aryan Gaikwad - 5 years, 10 months ago

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it asked for lines which is 1 dimentional

Akash singh - 5 years, 10 months ago

Yes 1 thick line should be the correct answer because the pen thickness was not specified in the question

Tanner Eckmann - 5 years ago

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This works because it says use a pen c:

Nicolas Gosselin - 5 years ago

Indeed, although note that it can be done with only three lines if they are extremely long and at a slight angle! Also only one line if you bend the paper.

Caleb Townsend - 6 years, 4 months ago

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I know right!!!! I wanted to do 3, but I figured it wouldn't be it though.

Levi Heath - 6 years, 3 months ago

In my own analysis "THREE LINES" is the right answer because the problem didn't mention that all lines should be connected with one another.

Fahmar Daño - 5 years, 12 months ago

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Your pen can't be removed from the page

Katherine Killam - 5 years, 5 months ago

It did state you cannot lift your pen

Christopher Uphoff - 5 years, 11 months ago

those wold be curves

Akash singh - 5 years, 10 months ago

... You can beat it with 3 lines... All you need to do is go from the bottom of one colume out past the second one making a point beyond the second lines.. and down the again at the bottom of the third line.. But that was only taught to me in my LOGIC CLASSES when i was in 7th grade.. Its not like it matters here or anything....

Dani Cykodic - 5 years, 8 months ago

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Things become a bit more advance when we speak about 0 dimension dots. Unlike the usual problem this do not have a thinkness. But still according to the rules indicated in this puzzle, it can be solved with 3 lines. That is by connecting the 3 dots in each line then have a curve to the next line and repeat the method.

Sajith Perera - 5 years, 2 months ago

This question is a classic puzzle ! Still, nice solution bro.

Venkata Karthik Bandaru - 6 years, 4 months ago

the question is not an appropriate one. while setting questions, you must mention what you want specifically, related info's, clues and most importantly the conditions that must be satisfied. Consider my comment as a suggestion. i really respect your wisdom.

Rafjany Yasar - 6 years, 3 months ago

It's not a line. As per this logic any number of points can be covered with one "line"

Ramesh Sridharan - 5 years, 5 months ago

O thought 1 link cause ias a 0 dimensional objeto and thinking out of the box o bended all of it in a single line. LOL

Cristiano Vargas - 5 years ago

The answer is wrong! You can do it whit one lane: If the points are near, you can do it whit one pencil, and if the pencil thick is big, and I mean so big, you can do it as well whit one lane

Some &Body - 5 years ago

The answer is zero. You can just use curly lines

Ken Kan - 4 years, 9 months ago

Answer can be lots of number you choice in any geometry you choose. You did not define anything by saying the points are 0-d Even zero lines is an answer. The points can all be on top of one another.

Richard Sinclair - 4 years, 4 months ago

It doesn't say all the lines have to be connected tho does it? Couldn't you just make three straight lines one over each row of dots

Scott Taylor - 4 years, 3 months ago

Frankly speaking the question itself is poorly drawn up, and secondly you are all wrong. In a 0-dimensional world you could fold the "page" in triples and ONE line would cross all nine points at their EXACT coordinate. Do any of you think?

David Bloom - 6 years, 3 months ago

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We are all here because we enjoy thinking. Rudeness is unnecessary.

Tatum Boyle - 5 years, 5 months ago

In here only the dots(spots) are 0 dimensional. Therefore the flaw in the question isn't there but that it should mention that only straight-lines can be drawn.

Sajith Perera - 5 years, 2 months ago

Straight lines? 3

http://ncpm.me/dmgk

Mentor Neto - 5 years, 7 months ago

You can bend the space around the dots to a point where all dots are connected without any lines.

Paul Schafer - 4 years, 11 months ago
Farouk Yasser
Feb 16, 2015

This answer is wrong, it can be done with only 3

Moderator note:

This solution has been marked wrong. We are treating the spots as a 0-dimensional object.

Not really, here you have thick points....a line must pass by a point center to consider it passing by...If you do not pass your lines by their centers then your answer is wrong

Ahmed Mouloudi - 6 years, 3 months ago

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Nowhere in the question does it indicate that the lines have to pass through the midpoints of the points or the correct "Thickness" that these lines should be so your argument is invalid.

Here is the question again: What is the least amount of straight lines needed to cover all 9 spots if you were using a pen and it could not be removed from the page?

Edit: hell, like someone mentioned below you can just have one thick line that goes through all these dots!! This question is seriously a joke!!

Farouk Yasser - 6 years, 3 months ago

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point is generally dimensionless and ideally thickness should be zero but that would make the points not visible.....

Irtiza Zafar - 6 years, 3 months ago

Hey you know I saw this question on a TV show and they did it with 4 lines and after that they showed that it can be 3 also as u showed........so I agree with you.

Rishabh Kumar - 6 years, 3 months ago

What if the lines are infinitely long?

Aryan Gaikwad - 6 years, 3 months ago

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still it would be parallel

Akash singh - 5 years, 10 months ago

probably because there is the hidden assumption that every spot isn't "thick", in a sense

Eric Escober - 6 years, 3 months ago

What i said!

Hafizh Ahsan Permana - 6 years, 3 months ago

He had already mentioned that the dots are of 0 dimensions so if you draw lines as shown in your figure those lie parallel rather than intersecting.

Siddhartha Vasireddy - 6 years, 3 months ago

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This solution was posted before the question Excerpt was changed. Before it just said: lines through these spots without any mention to their dimension hence why I wrote this for him to change the question Excerpt. :)

Farouk Yasser - 6 years, 3 months ago

concept there is sientific not mathematical. two parallel lines meet at infinity like rays of sun but mathematically answer would be 4. but iam impressed .

Rajat Pathak - 6 years, 3 months ago

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Sorry but no parallel lines meets at infinity. Sun's rays are not parallel at all. But we humans perceive it as parallel due to the distance. In any case while this is an ideal condition what you said will never happen.

Sajith Perera - 5 years, 2 months ago

Thinking outside the box there, however there is no L or W for the dots...

Matthew Gorman - 6 years, 3 months ago

The dots are mentioned as o-dimension, it has no height or width. If you want to pass three lines you have to draw the lines up to infinity (which is practically impossible). Because the lines should be parallel to pass through the each point and the definition of parallel lines is the lines which cut between themselves in infinity are called parallel line. So the answer is 4.

Trishit Chandra - 6 years, 3 months ago

0 dimensional.. don't have length or width .. Mesa mesa

Mohamed Ashraf - 6 years, 3 months ago

It looks a bit odd this way.....

Deep Chatterjee - 6 years ago

If this solution is treated as correct the lowest answer is actually one as you can spiral from the centre point and hit all 9. As it wants the answer 4 the assumption is that the lines must pass through the centre.

Anthony Guarnieri - 5 years, 8 months ago

Thank you!!!

Dani Cykodic - 5 years, 8 months ago

We should consider the dots as tiny dots and u have done it wrong. If ur thing is right then enlarge the dots such that only one line can Traverse all the dots. The dots should be connected by a horizontal or a vertical line that's it

Ganesh M S - 5 years, 5 months ago

Maybe the lines should only horizontal, vertical, and diagonal.

Jansen Wu - 6 years, 3 months ago

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Again it should be clearly shown in the question excerpt that this is the case. we shouldn't just guess what the rules are!!

Farouk Yasser - 6 years, 3 months ago

Yes, It could be 5 also

Anny Ahmed - 6 years, 3 months ago

Isn't that off the paper?

John Wang - 6 years, 3 months ago

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removed, ok, not off paper

John Wang - 6 years, 3 months ago
Olawale Olayemi
Feb 12, 2015

Solution is to literally think outside the box by drawing a line across one of the sides and extending it till another imaginary point outside the box from where we can draw a line through two more dots till another imaginary dot on the adjacent side of the square of dots. From there only two more lines are necessary to finish the job

WTH!! 3 if you read the instructions correctly If i did of course..???????

John Dowe - 5 years, 4 months ago
Kyle Chormanski
Aug 26, 2016

I can do it with one big thick line that covers all nine dots at once. Nothing in the prompt says the line has to be thin or anything.

Baldha Mulji
Sep 11, 2016

I have no solutions

Emmétt Nash
Jul 18, 2016

Since it doesnt say you can't back track, i took it as 4 be making a E shape. Overall its still 4 lines...

you can also solve this with three lines easily!

Matt P
Jan 13, 2017

Tarmo Taipale
May 31, 2016

The 4 move solution is incorrect because then you move out from the page, and that was forbidden!

we don't know where the ends of the page are

Deepthi Unnikrishan - 5 years ago
Brett Williams
May 13, 2016

You can connect all the dots using three lines, three diagonal lines would cross each point but would be sloping so that the next diagonal would cross the next three dots and then the same for the final line

We could draw them ddiagonallyand one line on other diagonal

Niliansh Sinha
Oct 9, 2015

I could even join those using just 3 lines!!!!!!!!!! theorically....join 1st three dots (kept horizontal) through a st. line take it to infinity(as st line can extend to infinity) IIIy draw line 2 & 3 through another set of 3 dot as u must be thinking u need 2 lift up your hand for that but no.......... as we know parallel line meet at infinity so if u start from 1st dot (at top extreme left in pattern) and continue to +infinity (along +ve X direction) & from there drawn a parallel line passing through 6th point continuing to point no. 4 and then moving 2 -ve infinity and from there drawn another parallel line crossing through 7th point & so on to point no 9...........Conclusion: we can join the 9 dot pattern just using 3 lines, but the ans depicted is 4 which is false as proved above

Jason Proffitt
Sep 29, 2015

rules need to specify that you can touch any one dot more than once

Ryan Taylor
Sep 8, 2015

Using a normal pencil sized line it can actually be done in three. Start way out side on top and cut across the top of the top left, the middle of the top middle and the bottom of the top right and extend the line past the dots and do the same thing back and back again

A line has the same thickness as a point. All a line is is a bunch of points strung together.

Austin Fix - 5 years, 6 months ago
Ruhan Muzaffar
Sep 3, 2015

Fussion of (+)and (×)

Adarsh Baderia
Jun 30, 2015

In my opinion 3 will be the correct answer not 4. You can join all th three lines by making a W or M including all the 9 dots.

Gunin Jain
Jun 8, 2015

extend the lines beyond the given points and you will get the answer

Abhishek Pokala
Feb 16, 2015

We could get it in 3 lines, though.

1 2 3
4 5 6
7 8 9 .

1-->4-->7. From 7 (i.e., the bottom dot in the first column), you go to 2 (i.e., the top dot on the second column). From 2-->5-->8. From 8, you go to 3, then 6 and then 9.

but that would become 5 lines !

Heeral Dedhia - 6 years, 3 months ago

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Oh, right, sorry. :| My bad.

Abhishek Pokala - 6 years, 3 months ago

Slanting lines are considered to be straight lines,

Frank Sarte - 6 years, 3 months ago

thats 5 again

Rajat Pathak - 6 years, 3 months ago

7to2 and 8to3 you have to go with lines itself.For you its not 3 its 5.

Arjunesh Namboothiri - 6 years, 3 months ago

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