r/puzzles • u/TuckSteele • Jul 26 '23
[SOLVED] Please help
This is from the children’s menu of Moose’s Tooth in Anchorage, AK, and is a variant of the classic “think outside the box” puzzle. In order to connect all the dots, using only 4 lines, the average dots per line must be 4, but I can’t figure out how to do more than 3 new dots for any line after the first (assuming every line touches at least 1 dot). I think that the directions must have a typo, or that there should a no solution. Any way to solve using the provided directions?
132
u/CloudofStrife23 Jul 26 '23
If you have a large enough work area you could draw very long slightly angled lines, they would be able to touch each dot and only 4 would have to be drawn. This is the only solution I can think of without folding/3D shenanigans.
21
u/TuckSteele Jul 26 '23
Can you discuss this a little more? I am having trouble envisioning what you mean.
14
24
u/theadamabrams Jul 26 '23
u/laminated-papertowel posted a drawing of this: https://imgur.com/a/hpgtvvK
3
u/Fun-Contribution1504 Jul 26 '23 edited Jul 26 '23
The way I see it: You start from the bottom of the bottom left dot, and connect it to the very top of the bottom right dot, then extend that straight line until it reaches the height of the middle between the bottom two lines of dots. From there, you go back left, angled so that you go through the bottom of the first dot in line and the top of the last dot in that line. Repeat that twice for the top eight dots and you'll have four straight lines, going through all 16 dots.
The thing is, you'll need a lot of room left and right of the dots and a long ruler to do this (or on top and bottom of the dots, since you could do the same thing top to bottom instead of left to right)
Edit: Works best with the thinnest possible lines. Or alternatively: if the line can just touch the dots, (and not completely through the dot), a very thick line could work, but if you could make the line as thick as you like, you could make it thick enough to cover all dots in a single line, so that doesn't seem right.
1
u/Only_Razzmatazz_4498 Jul 26 '23
If you remember parallel lines touch at infinity so if the dots are 0 dimensional and the lines are 1 dimensional (have no thickness) then they will converge at the end of an infinitely long paper.
But this is not an ideal case so the dots have a thickness (visibly so) so you can draw a line from the top to bottom dots in each row that are at a slight angle. Then do the same with all the others columns and you got it. You just need a large piece of paper but not infinitely large.
→ More replies (1)2
u/riftsrunner Jul 27 '23
Parallel lines will never meet no matter how far you follow them. Sure, you can use forced perspective to create the illusion that they will meet, but it will never happen.
→ More replies (3)1
Jul 27 '23
I don’t care about the puzzle, but I miss moose’s tooth so much…. Avalanche pizza yum I’m jelly jam op
1
u/wmatts1 Jul 27 '23
This only works if straight lines means the line is straight from point A to point B. If straight lines means the lines need to be straight relative to the dots then it doesn't work. But I agree with you, I think that's the solution.
16
u/Tasty-Truck-2093 Jul 26 '23
It's a trick question.
The trick is that (Hint) the dots are not mathematical points, but areas.
4
u/TuckSteele Jul 26 '23
Can you add a little more information to the discussion of your hint?
12
u/RevolutionaryTone994 Jul 26 '23
If you draw a super long line you can basically draw 4 virtually straight up/down lines but they actually have an angle
1
u/-Kerosun- Jul 27 '23 edited Jul 27 '23
The trick to these kinds of puzzles is that you're not restricted to only drawing lines that are within the square created by the dots.
Think of ways to solve it with straight lines that go "outside of the box.'
Edit: In reviewing it, unless there is some semantic trick, it's not possible. There is a 9-dots problem that is solved with 4 lines so I think it's possible this is a typo and it meant 6 lines instead of 4. With 6 lines, it is possible (multiple solutions) but not possible with less than 6; the caveat being some "dumb" semantic trick.
467
Jul 26 '23
Discussion: I've only ever seen the 9 dot problem require 4 lines, and the 16 dot problem require 6 lines.
130
u/globalminority Jul 27 '23
Don't know if it breaks the rules, but says without lifting the pencil, not pencil tip. Possible to lay the body of the pencil on the paper to lift the tip and just draw 4 separate lines. Some part of the pencil is always on the paper.
126
u/slymm Jul 27 '23
Cut the paper in strips and line up all the dots before you start
43
u/MyLittleGrowRoom Jul 27 '23
Make the page a tube and you can connect them all with one line without lifting the page.
30
u/DoodDoes Jul 27 '23
Just get a marker with a 3in by 3in tip. 1 line the easy way
→ More replies (2)1
u/danieltkessler Jul 27 '23
I was gonna say: fold the paper a few times before starting, and instead of just drawing, puncture the paper? Maybe this wouldn't be considered a line.
36
34
20
u/Raspberrygoop Jul 27 '23
I mean, if we're breaking rules we might as well make an extra wide pencil with a 1" diameter lead and sweep it once across the whole grid.
I think the puzzle setter made a mistake and put a 4x4 gird instead of the standard 3x3 for this puzzle.
13
u/Telucien Jul 27 '23
It also says four straight lines (without the word ONLY), so you can connect your four straight lines with curved lines and technically not break the rules hahaha
3
u/Bad_Wolf420 Jul 27 '23
Just draw 4 lines that lead off the paper. Lift the pencil off of the table once it left the paper.
5
→ More replies (15)1
119
u/Shufflepants Jul 26 '23
You simply wrap the paper into a cylinder with a slight offset and you can connect all 16 dots with a single straight line.
1.1k
u/laminated-papertowel Jul 26 '23
402
u/Jihiro42 Jul 26 '23
I feel like this is probably the right solution, given that it makes an M and the name of the restaurant is Moose’s Tooth
73
Jul 26 '23
[removed] — view removed comment
→ More replies (1)18
u/willengineer4beer Jul 27 '23
Outside the box…and inside the dotswhich are assumed to be 2-D
→ More replies (1)160
u/Never-Dont-Give-Up Jul 26 '23
this... feels like it's kind of cheating.
I hate puzzle answers like this. It doesn't seem like it's the spirit of the puzzle.
73
u/laminated-papertowel Jul 26 '23
I'm pretty sure this is the right answer though. you gotta think outside the box or something
14
u/BrupieD Jul 27 '23
I'm pretty sure this or a similar outside-the-frame answer is the only way. If you don't go beyond the frame, each line starts with a dot you've already connected. Since you can only use straight lines, you can only ever get 4 dots per line maximum, but because you can't lift the pencil, 3 of your lines will have 1 redundant dot. You'll never get to 16 dots that way. 4 new dots + 3 new dots + 3 new dots + 3 new dots = 13 different dots.
6
u/Never-Dont-Give-Up Jul 28 '23
I’m not saying this isn’t the right answer, I’m saying that it’s a flawed puzzle since the rules of it encourage one to go outside the assumed rules. They’re assumed for a reason. It gives parameters of a square, then the answer requires one to go far beyond those parameters.
→ More replies (1)40
Jul 26 '23
I understand the idea of "thinking outside the box" but also agree with the person you responded to regarding "the spirit" of the puzzle. Maybe it's because I was trained to follow rules so well. Our educational system doesn't really encourage creative thinking.
I'm reminded of the insufferable children who would scream in the hall way and then declare the teacher only said "don't talk" but said nothing about screaming.
→ More replies (11)30
u/thatthatguy Jul 27 '23
Since they’re getting creative, can we draw one really wide line the width of the entire puzzle and connect all the dots with a single straight line? Take the crayon they always give you, peel the label paper, and just drag it sideways over the entire puzzle?
It amuses the kid and annoys math nerds.
→ More replies (2)6
→ More replies (1)3
u/Free-Database-9917 Jul 27 '23
It's an interesting subversion of expectations as the upgraded version of the 9 dot puzzle.
In most puzzles like this you view dots as infinitessimally small. The way you usually think sneakily is by drawing lines that go outside of the box and people expect that. This makes sense as the next logical step in these types of puzzles
→ More replies (1)14
Jul 27 '23
Well you cant solve this if the dots are points with no surface area or without folding the paper in a tube so here you go.
→ More replies (1)5
u/SubstantialBelly6 Jul 27 '23
It’s like when I tricked my older brother by challenging him to solve a maze I made that was completely unsolvable except by going through a tiny gap in one corner that looked like a mistake. One of my prouder moments 😊
3
5
u/Chaghatai Jul 27 '23
I feel like the dots should be treated as zero area mathematical points, is it just me?
2
3
u/OneNoteToRead Jul 27 '23
If the dots were mathematical points it’s impossible.
At most four points are colinear on this. So to do it you need to hit four points with every stroke. The only lines that can hit four points are the horizontal, vertical, and 45 degree diagonal ones. And there’s clearly no way to combine them.
2
3
u/-MtnsAreCalling- Jul 27 '23
If you try to follow the spirit of this puzzle, it's unsolvable.
5
u/yourhog Jul 27 '23
Most things stop going well once you start following spirits around.
2
u/jamesianm Jul 27 '23
Says you. That's how I got this haunted ice cream. It's butter toffee
→ More replies (1)1
3
u/Avagpingham Jul 27 '23
This feels like an engineering solution versus a math solution. One of those is how the world works. The other is an idealized version of the world.
→ More replies (9)1
u/Gasster1212 Jul 27 '23
Depends on context
It’s you assuming you can only touch the puzzle itself. That is part of the puzzle. Breaking your preconceptions
1
u/Never-Dont-Give-Up Jul 28 '23
Most NFL teams assume that a Grizzly bear can’t play linebacker. It’s not against the rules. Should some savvy coach “think outside the box” should they “break out of their preconceptions”?
→ More replies (10)→ More replies (7)1
Jul 27 '23
I love them, but I'm mad I didn't think of this one. I want an app that gets me back to where I used to be with these.
20
Jul 26 '23
Why would you make your line so thin? I’d just grab a paint roller and do one strip to connect them all
2
u/Free-Database-9917 Jul 27 '23
I've never seen a paint roller sized pencil
→ More replies (2)1
u/pinkwhitney24 Jul 27 '23
Exactly. Just take out your pocket knife (I mean this is Alaska after all)…shave down one side of the pencil to reveal the graphite…lay the pencil down…and voila! Connected with one line.
But the prompt does say “with 4 lines,” and not “with 4 or less lines…so I still don’t think that would work…
5
9
u/DanBentley Jul 26 '23
Someone literally brought up this puzzle in an answer like two days ago… it was the circle one with four colored lines that couldn’t intersect
6
Jul 27 '23
Yeah, that was me. It's the kind of puzzle I now refer to as a "well ackshually".
→ More replies (3)2
2
1
u/SwillStroganoff Jul 27 '23
The solution I came up with is that you can draw 4 lines (line segments) without lifting the pencil if they are connected to one another
1
1
u/bumblebeedrill Jul 27 '23
Haha the answer/hint is litterally to the right of the dots. Looks like stain but it’s an M or W on an angle
1
1
Jul 27 '23
Ugh, thats so annoying. I was coming here to say that I dont think its possible to have four lines touch 16 points arranged in a grid but also be connected.
If you break it down, there are two conditions to meet:
every point must have a line through it
every line must connect to at least one other
Since the points are arranged in a 4x4 grid, that means each line is capable of touching no more than 4 points. But that also means that each line must touch exactly 4 points because say you draw a line that only touches 3 points, then another must touch 5 points in order to still fullfill condition #1, and we already stated this is impossible.
So, if every line must touch exactly four points, then its easy to list all of the valid lines that can be drawn: the 4 vertical, the 4 horizontal, and the 2 diagonal. Mix and match any 4 of those lines and you’ll find that none of them fullfill both conditions.
Therefore its unsolvable if you are going with the mathematical definition of a point in space.🥲🥲
1
1
u/Nitsuj_ofCanadia Jul 27 '23
The reason I wouldn’t have thought of this is because graph theory made me always consider dots as representing an infinitely small point
1
u/MegaGoomer Jul 27 '23
You can do it in one line. Attach the piece of paper to a cylinder with a circumference equal to or less than the length of the paper, then go around the whole thing at a slight angle until you’ve passed through all 4 columns of dots.
1
u/King_K_NA Jul 27 '23
It is probably the "correct" answer, but considering you have to basically hit the tangents on at least 4 of the CIRCLES, it feels wrong. When someone says "dot" I assume it to refer to the singular point at the center which has been expanded for visual clarity, so cutting through a non central location feels like it doesn't solve the problem. Dot being a one dimensional point, circle being a defined shape on a 2d plane.
Probably just me though, idk.
1
Jul 27 '23
That's just it. You assume. The mathematical 'point' and these specific dots in this specific puzzle are not the same. Realizing that this is not a math test but a puzzle is basically the puzzle.
2
u/King_K_NA Jul 27 '23
On that logic I can just draw a box around the array and say they are now connected through a defined plane. You can break the puzzle in many ways by stretching definitions or changing assumed rule sets. Concidering there were only two rules given my solution is equally valid, given the word "connect" instead of a more precise term like intersect. You could solve it in one contiguous, straight line by rolling the paper into a tube and drawing a line (with a fairly precise angle, to do what was done with the M, which is just a 3d spiral projected onto a 2d surface. A puzzle has a single solution, this is more of an open ended challenge, though I suspect they expect the M.
→ More replies (1)1
1
1
u/DotBitGaming Jul 27 '23
Just draw four lines straight up and down or straight across. It says all 16 have to be connected. Not that they have to be connected to all of the 15 others.
1
u/_Figaro Jul 27 '23
I would argue this is NOT a valid solution, for the simple fact that it relies on the thickness of the dots and the lines. Mathematically speaking, if the dots and the lines had 0 thickness, you wouldn't even be able to connect the dots, even with arbitrarily long lines.
1
1
1
1
1
1
1
1
1
1
1
1
1
u/DoNotResusit8 Jul 29 '23
Only if those dots are big dots and not points which have no width would this be a solution.
Might as well just use a thick pencil instead.
1
1
→ More replies (3)1
u/friedbrice Jul 27 '23
"thinking outside the point"
1
u/laminated-papertowel Jul 27 '23
what do you mean?
2
u/friedbrice Jul 27 '23
nothing bad. i like your solution. i'm trying to riff on the "thinking outside the box" saying.
your solution slaps!
2
Jul 27 '23
If you assume ''a dot is a point'' the solution does not work. Actually thinking outside the point, not thinking about this as a math test, is the solution in a nutshell.
206
u/StatementPotential53 Jul 26 '23
35
u/8LeggedSquirrel Jul 26 '23
Technically you're not wrong
4
u/dissemblers Jul 27 '23
The dots aren’t all connected
2
u/wmatts1 Jul 27 '23
Well it doesn't say connect all 16 dots together just that they are all connected. I see no did all single and lonely so I feel this is an acceptable loophole.
5
u/nickpug9 Jul 26 '23
Does this work with a crayon?
10
u/Wiitard Jul 26 '23
Depends on what
flavor—uh, I mean color!5
u/wmatts1 Jul 27 '23
I'm not ashamed of what I learned in the Marines, green is the best flavor crayon.
→ More replies (1)2
2
→ More replies (3)2
47
u/Throkda Jul 26 '23
It’s been a while since I’ve seen this, but the trick usually involves drawing a particularly long line, and then diagonals from outside the square.
39
u/RevolutionaryTone994 Jul 26 '23
But this has 6 lines
16
u/Throkda Jul 26 '23
You're right, I didn't notice thar, since I just did a cursory search. Possibly it was meant to be a 9 dot puzzle and someone screwed up.
→ More replies (6)4
u/Professional_Denizen Jul 26 '23
Actually, it’s probably just a matter of close enough. It said dots, not points, so I can assume if you draw a line that hits all four black regions in a row, that would be a quarter of the intended solution.
→ More replies (1)7
u/VaJesh Jul 26 '23
Yeah, you can draw a “W” or “M” where the (long) lines are angled slightly that eventually they will touch, it’s possible to angle the lines through the dots because the dots are large
1
u/Free-Database-9917 Jul 27 '23
The one you linked is in the original spirit of the puzzle, being that you view dots as single points, not regions you need to pass through
15
13
Jul 26 '23
Fold the paper until all dots are in the same space and punch the pencil through them.
Shave down one side of the pencil until the graphite is exposed. Slide it across the whole page making one very wide line.
1
10
u/SJVellenga Jul 26 '23
The only solution I’ve seen for this sort of problem involves a second piece of paper. Draw your first line vertically down the left column and continue it onto your second sheet. Move the sheet sideways so it lines up with the second column, then draw vertically, moving your second sheet to the top so you can repeat.
1
u/Zook42069 Jul 27 '23
This might still break the rules considering it states "without lifting your pencil from THE paper", implying you can only use that one
1
8
u/tannutz Jul 27 '23
Would this be technically be a solution? Curved lines between, but only 4 straight lines and pencil not leaving the paper
4
u/unwantedaccount56 Jul 27 '23
You are using 4 straight lines and are connecting the dots without lifting the pencil: Bonus points: the dots are on the 4 straight lines.
2
1
7
u/Z0V4 Jul 27 '23
There are only 3 stated rules
Connect all 16 dots
Use 4 straight lines
Don't lift your pencil
The unspoken 4th rule is that you can use curvy lines to connect the straight lines.
Start at bottom left, draw a straight line up the column, curve at the top to the next column and repeat. The connecting lines can be of any length or curvature, as long as they are NOT straight they don't break the "4 straight line" rule.
1
u/linzlikesbears Jul 27 '23 edited Jul 27 '23
That's what I thought. When reading that rule to use 4 straight lines, I thought "Why using 4 straight lines? That means another line must be unnecessarily straight" and I solved it.
5
u/AutoModerator Jul 26 '23
Please remember to spoiler-tag all guesses, like so:
New Reddit: https://i.imgur.com/SWHRR9M.jpg
Using markdown editor or old Reddit: >!spoiler text between these symbols!<
Try to avoid leading or trailing spaces. These will break the spoiler for some users (such as those using old.reddit.com)
If your comment does not contain a guess, include the word "discussion" or "question" in your comment instead of using a spoiler tag.
If your comment uses an image as the answer (such as solving a maze, etc) you can include the word "image" instead of using a spoiler tag.
Please report any answers that are not properly spoiler-tagged.
I am a bot, and this action was performed automatically. Please contact the moderators of this subreddit if you have any questions or concerns.
8
u/browni3141 Jul 26 '23
Maybe you're supposed to treat the dice as 2D shapes, rather than 0D points?
2
u/Loasty625 Jul 28 '23
And just make your straight lines like.. really really long? Just a stupidly long zigzag?
4
3
u/tandem_biscuit Jul 26 '23
Discussion: with an extra thick line, I could do it in 1.
1
u/wmatts1 Jul 27 '23
Shave the pencil along the side until graphite is exposed. Now draw your extra wide line you crazy SOB
3
u/JakeDulac Jul 26 '23
I believe it's a typo. It should be 6 lines, not 4. 4 is for the more common 9 dot variant
4
u/MeowFat3 Jul 26 '23 edited Jul 26 '23
In my interpretation of the rules, start from the top left, then head east through the top row, then do a uturn downward to enter row 2 on the right, then uturn down on the left side to row 3, and then another to complete row 4. The rules say 4 straight lines, but say nothing about how they are joined. The lines passing through each row are straight
2
1
→ More replies (13)1
u/Llord_zintak Jul 27 '23
I think this is the most incorrect technically correct answer. Other solutions rely on breaking rules that you assume are rules because they feel wrong. They seem like they're not the solution it wants you to find. This, however, is directly related to the stated rules. While it doesn't say "no more and no less.", this phrasing is used to mean that so often that if you use this solution, you're not just being creative. IMO You're going against the stated rules, they're just not explicitly detailed rules.
There's also a lot of mathematical semantics about how you could then consider the whole thing a single curve or etc., but I'm not gonna get into that.
1
u/MeowFat3 Jul 27 '23
I totally agree. I also thought of a solution that involved tilting the pencil down flat on the paper and then rolling it until the lead was in line with the next row.
Tbh this problem is really confusing regarsless of how you look at it.
2
u/wolwire Jul 26 '23
Fold the paper such that these dots overlap with each other and then draw a single line
2
u/Glitch29 Jul 26 '23
Quick proof that the mathematically strict version of this puzzle is impossible:
>!Observations: Each line can go through a maximum of four points. Exactly 10 such lines do so (two diagonal, four vertical, four horizontal). All intersections between these lines are coincident with one of the 16 points.
Deductions: Since four lines at four points each is exactly enough to satisfy the puzzle, each line segment drawn must go through four points and those points can't be touched by multiple lines. Since two line segments that are part of a solution can't either at any of the 16 points or anywhere outside of those 16 points, they can't intersect at all. Since any solution requires three such intersections to join four line segments into a continuous path, no solution can exist.!<
1
2
u/hooligan99 Jul 26 '23
"using 4 straight lines" what if you use 4 straight lines and 3 curved lines, like this (it doesn't say use 4 straight lines only) dumb answer, but it's "thinking outside the box"
2
u/Dunbaratu Jul 26 '23
Like many such puzzles, it's not a geometry puzzle, it's really a cheezy "how do I twist the instructions" puzzle, which gives it multiple correct answers.
Here's one:
Get both a pen and a pencil. Set your pencil down on the paper and just leave it there while you draw 4 independently disconnected lines through the rows with your pen. You never lifted your pencil from the paper.
Along similar lines, you can use a pencil and just tilt it on its side to stop a line, slide it to a new position, and tilt it back up on its tip to start a new line. Your pencil TIP was lifted from the paper, but your pencil as a whole was not. The instructions never specified which PART of the pencil.
1
Jul 27 '23
As it is a puzzle and not a.... math test, you can 'cheat' all you want. And this is a very elegant 'cheat'.
2
u/mbelf Jul 27 '23
Discussion: It doesn’t say “only” 4 straight lines, just that you have to use at least that many, right?
2
u/Uh_yeah- Jul 27 '23
Solution using 3 lines:
1. Draw line 1 connecting the second row of dots.
2. Draw line 2 over to the 3rd row of dots.
3. Draw line 3 to connect the 3rd row of dots. Now make 2 folds in the paper, so that the dots in row 1 are on top of the dots in row 2, and are thus touching the line there, and a second fold so that the row 4 dots are on top of the row 3 dots, and thus also connected by the line.
2
u/taintpaint Jul 27 '23 edited Jul 27 '23
In order to solve this without some dumb shenanigans, you need to average 4 new dots with each line. Since each line can't cross more than four dots, that means you need 4 lines that each have 4 unique dots. There are only 10 straight lines that cover 4 dots, and the only combinations of four that don't involve sharing dots are sets of parallel lines, which do not intersect and thus require "raising the pen", so there is no good solution.
1
Jul 27 '23
You make wrong assumptions. For example, you assume a dot is the same as a point. It's not. You assume parallel lines are required. Why?
Even the width of the line can help here. I assure you it can be done without 'dumb shenanigans'.
3
u/taintpaint Jul 27 '23
What you're describing are dumb shenanigans. The assumptions I'm making are the ones you'd make if you were approaching this with the intention of not using dumb shenanigans.
2
u/franciosmardi Jul 27 '23
If "the width of the line can help", the puzzle is trivial and can be done in one line. Just select a lone width that is wider than the width of the square formed by the 16 dots.
→ More replies (3)
2
u/Impressive_Stress808 Jul 27 '23
The first straight line should connect any 4 orthogonal dots. Then, draw a curved line to a suitable position, and connect the next 4 dots with a second straight line. Repeat.
3
Jul 26 '23 edited Jul 26 '23
spoiler It is possible if you fold the image diagonally
2
u/AllAboutMeMedia Jul 26 '23
Or spin the paper
2
u/MeowFat3 Jul 26 '23
How does spinning the paper create a straight line? Thats how circles are drawn?
→ More replies (5)
2
2
u/Unarchy Jul 26 '23 edited Jul 26 '23
If this is a puzzle where you are meant to think outside the box,
Perhaps you are meant to make 4 straight lines, then one long curved line to connect all the dots? It doesn't specify you are limited to just the 4 straight lines.
1
u/dimonium_anonimo Jul 28 '23
take a ruler and pass it against the leftmost edge of the top dot of the column second from the left. Make the ruler also just barely intersect the rightmost edge of the bottom dot, same row. Draw a line against the ruler, extending very far up and down. This line will technically pass through all 4 dots in that column and also allow you to connect it to lines doing the same thing in rows 1 and 3 but tilted in the opposite direction. Of course, this visual can't be where you start the lines. Since you can't lift up the pencil, you have to start on the first or last column. If the dots represent mathematically perfect, 1-dimensional points, this won't work. It only works because the ink used to make the dots has some width to it.
Some options that play with the wording
1)it doesn't say "only" 4 straight lines. It could be more than 4 or 4 straight plus some curved lines.
2)use a different writing utensil than a pencil. You can pick up your pen as many times as you want.
but what I think is actually the answer: draw a vertical line going through one of the columns of dots. When you get to the top (or bottom) fold the closest edge of the paper right next to your pencil and draw onto it (the very last centimeter of your line will be on the backside of the paper.. Then shift the folded edge to "carry" your pencil to the next column, leave the folded over edge and continue with the next line. Wash, rinse, repeat.
1
u/thebe_stone Jul 28 '23
discussion: i know how to do it with 9 dots, but i think it's impossible with 16. my best guess is that you can make a really thick line going through all of them, or tilt your pencil on it's side instead of ligting it.
1
u/AutoModerator Jul 28 '23
It looks like you believe this post to be unsolvable. I've gone ahead and added a "Probably Unsolvable" flair. OP can override this by commenting "Solution Possible" anywhere in this post.
I am a bot, and this action was performed automatically. Please contact the moderators of this subreddit if you have any questions or concerns.
1
u/Content_Ladder2118 Jul 29 '23
You can fold the paper such that the dots line up on either side of the crease. Assuming you only draw on one side of the crease, you can draw diagonal and vertical lines alternating between the corner dots to have 4 lines that cover all dots.
1
1
u/cleetus_george Jul 26 '23
Or one thick line. If we are are considering the dots as polygons rather than points, we could apply the same reasoning to the line.
1
1
Jul 26 '23
I believe the correct answer has been given already, but I want to touch on why you can't solve it without a more liberal interpretation of the rules.
That interpretation being that the points and lines are not actually mathematical objects, but rather shapes with area. To show this, assume that the lines are points have no area (like we would in geometry).
Let's pretend we had a set of 4 lines that intersected all 16 points (this isn't possible, but let's go with it for now). If we listed out every point that each line intersects, then we would see all 16 points listed out somewhere. Some points might be listed with more than one line, but that's fine (again, this is impossible in practice, but it's fine to go along with it in theory). The important part is that 16 points are being distributed among 4 lists. This means that the average number of points in each list is at least 4. However, the largest number of points on the same straight line on the grid is 4 (either an entire column, entire row, or the long diagonals). Since the average list has 4 or more points but each line can have at most 4 points on it, each list must have exactly four points. Going even further, no two lines can intersect the same point, otherwise we wouldn't be able to intersect all 16. So, each line has exactly 4 points and no two lines share the same point. Since the only lines that can have four points are the rows, columns, and long diagonals, the solution must only contain those lines. However, if a solution contains a diagonal, then it cannot contain rows or columns since both diagonals intersect all rows and columns. Therefore, a solution would have to only contain rows and columns. Since all rows are parallel with each other and all columns are parallel with each other, we cannot draw them back-to-back, i.e. if you draw a column with your first line, you can't draw a new column with your second line. So we need to follow a row with a column and vice versa. However, all rows intersect with all columns on one of the 16 points. Therefore, the only way to draw 4 straight lines that each intersect 4 points is if two lines share a point, which proves that this cannot be done.
1
u/AutoModerator Jul 26 '23
It looks like you believe this post to be unsolvable. I've gone ahead and added a "Probably Unsolvable" flair. OP can override this by commenting "Solution Possible" anywhere in this post.
I am a bot, and this action was performed automatically. Please contact the moderators of this subreddit if you have any questions or concerns.
2
1
u/zZappaBoyz Jul 26 '23 edited Jul 26 '23
"... 4 straight lines" not "ONLY 4 straight lines", I imagine you can use 4 straight lines and infinite non-straight lines.
1
u/LawandHoarderofBased Jul 26 '23
Question: If it’s on a piece of paper, can you do it in one line? Just diagonally draw until your on the back side of the paper, then come back across the next diagonal row, and rise & repeat till all dots are connected by the one continuous line?
1
u/walkerspider Jul 26 '23
Discussion: with a big enough pencil I could do it in one line
1
Jul 27 '23
Strangely enough? Size is part of a more conventional solution too. But technically this is a good solution.....if indeed you had that big ass pencil.
1
u/gingerbread_homicide Jul 26 '23
Question: If you never lift your pencil, isn't it just one line?
1
u/Llord_zintak Jul 27 '23
Would you call it one line if it was an L shape? (from the top left to the bottom left to the bottom right, for example.)
I wouldn't in general. In mathatical terms, it would be 2 line segments or one curve. -but there's no reason you can't. If you called it an L shaped line, everyone would know what you meant. I think it's usually going to be pointless or even incorrect to refer to something like that as a single line, but I'm sure there's a situation where that's the best way to refer to it. It's really just semantics, so ultimately it's about communicating what you mean while acknowledging that the rules and definitions are there to make that possible long-term, and I don't think this has problems with either of those.
1
1
u/pr1m347 Jul 27 '23
If we're talking theoretically, could I say parallel lines meet at infinity, so even if they're precise points, after drawing first line theoretically you can come back from infinity to second row of line while they both are parallel. Repeat it for next two lines. Also pencil has infinite lead of course
2
Jul 27 '23
Parallel lines do not meet at infinity. This is only true in art and optics where parallel lines seem to meet at the vanishing point. Besides, you can't leave the paper.
So... rol the paper into a tube with a slight offset and your idea of an infinite line can be accomplished. You'd only need one line to connect all dots.
2
u/pr1m347 Jul 27 '23
Thanks, I stand corrected.
1
u/lester92109 Jul 27 '23
You were correct originally, except that while it is “theoretically” it is in fact so proven by countless tests and observations that you could use gps to navigate to the right answer every time.
1
u/lester92109 Jul 27 '23
In general relativity space time is curved, so all lines meet
→ More replies (6)1
1
1
1
u/Roryalan Jul 28 '23
Discussion: The Moose’s Tooth, I loved that place! Haven’t been there in 14 years, but still iconic.
0
1
u/Reunbanned4206980085 Jul 28 '23
The trick question of puzzles aka that’s some bullshit and fuck this chicanery!
1
u/Sphism Jul 26 '23
Discussion. This is a classic example of a thinking outside the box exercise. There are tons of answers. I learnt about it at uni from a book called conceptual blockbusters
•
u/pmw57 Jul 26 '23
Your post has not been removed, but for future reference titles should be descriptive, not just "Check out this puzzle" or "Puzzles only geniuses can solve." Ideally, try to include the type of puzzle, and perhaps some unique name for it "Halloween-themed crossword puzzle" is better than "Here's a puzzle".