Solutions to Two Puzzlers About Drawing Lines

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9 жыл бұрын

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Пікірлер: 106

@mileslong9675 2 жыл бұрын

Funny story: Years ago, I was at a company seminar in which the nine dots “think outside the box” puzzle was presented. Like most of us who had been through these seminars, we knew what to do. I (along with my fellow employees) had drawn the nine dots on our blank sheet of paper. Out of boredom, I rolled mine up, since I knew what was next, but then I noticed something. I asked the boss if I could solve the puzzle in less than four lines. He said no, it’s not possible. I said it was possible, and then showed that if the nine dots are drawn on a sheet of paper which is then rolled up, the dots can be skewed in such a way that one straight line can spiral around the paper and connect all of them. My boss wasn’t too happy. I realized that the company wanted us to think outside the box, but not that far outside the box.

@TheBod76 2 жыл бұрын

You made a 2d "puzzle" into a 3d puzzle, that is not thinking outside the box that is changing the whole "puzzle". Also a if you bend a line around a cylinder it isn't strraight anymore.

@applmango 2 жыл бұрын

This is thinking outside the dimension

@pakde8002 2 жыл бұрын

Thinking outside the box is just a tired euphemism used by people who have no intention of leaving the box but want to seem innovative.

@SamuelPearlman 2 жыл бұрын

STAY WITHIN THE PLANE, EVERYONE!!

@GrandWushu 2 жыл бұрын

Bosses want you to be smart, but not smarter than them. That said, I hate those seminars. I've done so many of those survival prioritize the items scenarios which you can't really do because they never give you enough information up front.

@connyjohnson855 2 жыл бұрын

For the second problem you can just draw lines through the boxes, that won't break any stipulated rules 😊

@k.more1995 2 жыл бұрын

Thinking outside the box

@NorwegianQvirr 2 жыл бұрын

Connect the boxes though, not the letters. But yeah, technically not wrong

@cybore213 2 жыл бұрын

The topology of the solution will be the same.

@ryu9687 2 жыл бұрын

Bah gawd man

@cjvs1604 2 жыл бұрын

@@k.more1995 Well... through the boxes technically.

@smalaelefanten 2 жыл бұрын

"At most 4 straight lines" makes a solution far more easy to achieve than if it said "With only exactly 4 straight lines". Because in the first phrasing it means you could have less than 4, or no straight lines at all; meaning you could use curves between every single dot for a very quick and easy solution.

@tears_of_asariel3198 2 жыл бұрын

the phrasing is wrong in this video, but thats because it isnt supposed to be a trick question where you try and figure out a loophole.. if you were to try that, the person asking you to do this would just clarify after saying you can only use strait lines.. it wouldnt be a 'solution' it would be a misunderstanding of the rules

@JohnRandomness105 2 жыл бұрын

The second problem reminded me of a Sudoku "Cracking the Cryptic" puzzle, where Simon had to be told to "think harder" to connect two cells continuously without intersecting other lines. Once he was told that, I went back and spotted the snaky version.

@markhatfield5621 2 жыл бұрын

I remember a different version of the six boxes. Each of the top three boxes must connect to each of the bottom three boxes, no lines may cross.

@scottmcshannon6821 2 жыл бұрын

i came up with both the snaky version and the drawing thru boxes, which isnt against the stated rules. i thought the idea was to think outside the box without drawing outside the big box.

@denniscaswell2892 2 жыл бұрын

For problem 1, there is a way to connect all of the dots with just THREE lines. Part of the trick is to realize that the dots are NOT points, but have a definite size.

@smalaelefanten 2 жыл бұрын

Another trick is to have a large tip pen, then you could connect all with ONE line.

@EaglePicking 2 жыл бұрын

@@smalaelefanten Bring in the Monsterpen®

@TangoNevada 2 жыл бұрын

So a Paintbrush?

@vitrify 2 жыл бұрын

One line that goes around the world twice and a little more. ;)

@ryru2093 2 жыл бұрын

I've always thought of the "Super 'N'" with skewed lines. Same concept as the four lines, just to the extreme.

@dondee5439 2 жыл бұрын

The easiest way to understand and solve the second puzzle is to FIRST connect C to C in a direct line and then do the short snaked A to A followed by the longer snaked b to b. It can ALSO be solved by FIRST connecting the A to A in a straight line and then do the short looped C to C followed by the much longer looped B to B. Both of these solutions are just mirror images of each other.

@ozarkwheels4158 2 жыл бұрын

You can also do the second one with curved lines that go through some of the boxes. No rule against it.

@jamiedorsey4167 2 жыл бұрын

That's what I came up with as well. It just says you need to stay inside the big box.

@trumplostlol3007 2 жыл бұрын

Done. The second problem looked impossible at first. But after grabbing my pencil and paper, I solved it. If you can solve it without a pencil and a paper, then you have superb short term visual memory. LOL

@melkiorwiseman5234 2 жыл бұрын

It took me roughly 30 seconds of studying the picture and I solved it in my head.

@muzkat101 2 жыл бұрын

This is the first time I was the image of the A-B-C boxes; it was just too easy. The nine-dot puzzle is an old one; though, I do recall when I first saw it, I failed to solve it; that was when I was a young child -- I haven't forgotten the solution since.

@leahl5007 2 жыл бұрын

The dots puzzle didn’t say you have to connect the dots using straight lines. So just snake from one row to the next.

@q-tuber7034 2 жыл бұрын

Those are some funky-ass “lines.” Paths, maybe.

@neonjoe529 2 жыл бұрын

Yeah, bothers me too. If that’s a solution, then so is an oval that touches all six boxes…

@stanislavtodorov8705 2 жыл бұрын

Second problem - found the solution in 10 seconds. Guess drawing PCBs helps a lot hehe

@thomasmaughan4798 2 жыл бұрын

PCBs: Printed Circuit Boards

@musanim 2 жыл бұрын

In the second puzzle, if you start by connecting B with a straight line, there's no solution, since that line prevents both AA and CC from connecting. If you start by connecting AA or CC, there are three possible paths for B; of these, the ones that go around just A or just C block the third line, but the one that goes around both of them blocks neither, and that's the solution. The easy way to see why this works is to start with the positions of the free-floating A and C boxes reversed (so that you can draw straight lines connecting all three pairs), and then move A and C to the opposite sides while letting the connecting lines bend around them.

@matts1166 2 жыл бұрын

The puzzle is easier if you don't assume extra restrictions. No where does it way a connecting line can't cross a box that it isn't supposed to connect to.

@musanim 2 жыл бұрын

@@matts1166 Yes, and it's easier if you don't assume that the lines have to be in the plane of the paper, and not in 3-space.

@blackmber 2 жыл бұрын

That’s a cool way to visualize it

@matthewdancz9152 2 жыл бұрын

Oh pipe puzzle!!! I love those.

@396TurboJet 2 жыл бұрын

One person confronted with problem 1 just folded the paper in such a way that all nine dots were in a straight row. Then he just drew one line straight line connecting them all.

@currentbatches6205 2 жыл бұрын

Missed #1, got #2; that one had to do with release from the edge of the box.

@TonboIV 2 жыл бұрын

Your solution to problem 2 is correct, but very shallow. The thing to focus on, which I'm sure you know even if you didn't discuss it, is that this is a problem of topology. Since we can draw the lines with any shape, the position of the boxes doesn't really matter, nor even their shape or the shape of the border. All that matters is their letters, which ones are on the border, and in what sequence. Anything else can be changed by distorting the plane and the lines along with it. If we imagine the whole thing is drawn onto a super flexible piece of rubber, we could twist and stretch it until the loose "A" is on the left and the loose "C" is on the right. Now both "A"s are on the left side, both "C"s are on the right, and both "B"s are in the middle, so the lines to connect them up are easy to draw. After that, you can twist and stretch the other way, bending the lines into various weird snake like shapes which still maintaining the same connections. Once you realize you're dealing with topology, you can just move the two loose boxes to realize that the line from B to B passes to the right of the "A"s and to the left of the "C"s, then you can look at the original picture, and start with a line from B to B which loops to the right of the "A" box and then to the left of the left of the "C" box and you know that there will still be a valid path to draw the other two lines.

@isaac_aren 2 жыл бұрын

Happy with myself that I figured out the second one

@DLN-ix6vf 2 жыл бұрын

only reason I knew the first is because I have seen it before ! hence the term "think outside the box" :)

@yuwish6320 2 жыл бұрын

Ah, the second one got me. I knew what to do. Just didn't take it far enough.

@nbooth 2 жыл бұрын

The first puzzle can be done with 3 straight lines. (As long as the dots are not perfect points but have area.)

@billvojtech5686 2 жыл бұрын

If you define a line as a straight path between two points, the second puzzle is impossible. And putting it after the first puzzle, which specified straight lines, puts you in that frame of mind.

@pakde8002 2 жыл бұрын

Did you read the instructions carefully? Connect boxes with similar letters with lines. Lines cannot intersect. I wouldn't hire you.

@billvojtech5686 2 жыл бұрын

@@pakde8002 There is a technical definition of "line" which is: Roughly, we can say that a line is an infinitely thin, infinitely long collection of points extending in two opposite directions. When we draw lines in geometry, we use an arrow at each end to show that it extends infinitely. A line segment has two endpoints. It contains these endpoints and all the points of the line between them. You can measure the length of a segment, but not of a line. The "lines" being drawn to "solve" the puzzle are paths. I wouldn't work for you.

@paulroskilly4017 2 жыл бұрын

@@billvojtech5686 But it says connect boxes of the same letter with lines (plural), it doesn't say you can only have 1 line connecting 2 boxes, there can be multiple lines.

@billvojtech5686 2 жыл бұрын

@@paulroskilly4017 the "lines" as drawn are not actually lines. Those would be paths. Lines: kzfaq.info/get/bejne/fL15o82o3L2cc2g.html Curved paths: kzfaq.info/get/bejne/l7ynq911rdTNdas.html

@thomasmaughan4798 2 жыл бұрын

Topologically, the A's are on the left side of the path B to B, and the C's are on the right side of the path B to B.

@patrickpablo217 2 жыл бұрын

for the second, the problem doesn't say boxes of the same letter need to be *directly* connected, so you can just make one line that hits all the boxes without crossing itself (there are many options)

@Navajonkee 2 жыл бұрын

My immediate thought was "Wait, it didn't say the lines cannot go through the boxes"

@Nyrua 2 жыл бұрын

Thank you

@hughcdavies 2 жыл бұрын

My solution to the 2nd was like the internet join A to B to C to 2nd A, B, C and back to 1st A. It said connect the boxes, did not say directly, without going via the other boxes.

@VirginiaBikeWoman 2 жыл бұрын

No one said you can’t just draw right through the boxes.

@SoloPerICommenti 7 жыл бұрын

The second you can go through the boxes, without crossing lines

@mauijttewaal 2 жыл бұрын

My idea...

@eriktempelman2097 2 жыл бұрын

Problem 1 can actually be solved with just ONE line: wrap the paper around a cylinder, and there you go ...

@FreakinFred08 2 жыл бұрын

I don’t understand. Care to elaborate?

@peter9477 2 жыл бұрын

@@FreakinFred08 He's basically making the surface three dimensional (to wrap around at the edges) while claiming the "line" (curve) that could connect them all would still be considered two dimensional... bit of a cheat. (But these puzzles are often best solved with such a cheat!)

@klondike316 2 жыл бұрын

These problems are worded incorrectly. Easy to do based on the written rules.

@Mindraker1 2 жыл бұрын

The first puzzle: Take a really thick pen, crumple up the paper into a ball, and jab the pen through the paper.

@ejupbulliqi4069 Күн бұрын

how can i go from 1, to a,b,c and 2 to a,b,c and 3 to a,b,c without crossing line is posible

@naughtyskweet6 7 жыл бұрын

I drew the line from a to a through the upper b box. And from c to c through the lower b box.

@leif1075 4 жыл бұрын

I drew and DIAGONAL LINE FROM ONE BOX A to the other and it works!! Becuase I connected,the B's by going around C and A and the top right C going to the right around Box B and over and around Box,A to the bottom left C..e EQUALLY Valid Solution! Didnt anyone else do it this way??

@TomCee53 2 жыл бұрын

@@leif1075 yes, in fact, though he says there are many solution, there are topologically only 2 solutions, this and the one he described.

@jasonarthurs3885 2 жыл бұрын

Managed to solve 1st puzzle inside of a minute.

@shoppe99 2 жыл бұрын

I can do the first puzzle with ONE STRAIGHT LINE... Fold the paper two times so that the rows of three dots line up on top of each other. Then fold the paper again two times so they line up on top of each other again. Tack the paper up on a hay bale and shoot an arrow through all nine dots laying on top of each other. Just like folding time.

@applmango 2 жыл бұрын

Thinking outside the (2 spatial) dimensions

@thetexanbuzzsaw3145 2 жыл бұрын

For the second one you can just trace the edge of the box

@stoagymahalo5268 8 ай бұрын

What tye heck. I KEEP TRYING TO FIND THE ADVANCED ONE , where a HAS to connect to abc, and b to ABC and c to abc.

@xandermichels8336 8 жыл бұрын

1st also both of these took about 1 minute to do, harder questions?

@leif1075 4 жыл бұрын

The first one was hard be honest..and it was,worded badly..NOT ALL THE DOTS ARE CONNECTED TO EACH OTHER PRESH..PLEASE FIX WORDING..I cant be the only one who,thought that's what it meant and couldn't find the answer..

@raymond19001 2 жыл бұрын

I have a puzzle for you. All you need is a "dollar coin" and a piece of paper. Tear a small hole in the centre of the paper and ask someone if they can "slide" the coin through the hole without tearing the paper. The answer: place the coin on the table, put the paper on top of the coin with the hole directly above the coin, put your finger on the coin and "slide" the coin and the paper on the table.

@KSparks80 2 жыл бұрын

Same as pushing a beer bottle through a quarter sized hole in a napkin, without tearing it.

@maimaiiolivia2711 2 жыл бұрын

The big box is the thumnail

@bigdadjorel7151 2 жыл бұрын

too easy did in first try 5 seconds!

@rugershooter5268 2 жыл бұрын

I'm much dumber than the rest, I'd never got the second puzzle

@melhooker520 2 жыл бұрын

I did it without picking up my pencil

@leif1075 4 жыл бұрын

Didn't anyone else think the dots and lines meant all the dots had to be connexted to each other without a gap as in his solution?

@bobkrueger5910 2 жыл бұрын

Mathematician Euler proved many years ago that it can’t be done….

@docsavage8640 2 жыл бұрын

Fun

@salat6154 8 жыл бұрын

2nd comment lol

@NeverTalkToCops1 2 жыл бұрын

Second puzzle, you can just exit the small box and draw arcs to connect a,b,c. Nothing in the instructions prohibits this. You may thing there is a prohibition, but there is not. Another "outside" the box piece of asinine dog feces. Stop it. Stop it now!

@victorwizard8779 2 жыл бұрын

The answer is: Impossible

@tomasroca5139 2 жыл бұрын

The perpetual railway theoretically imagine because cellar italy guide by a weary nic. grumpy, spotless supermarket

@truejeffanderson 2 жыл бұрын

What does "Cannot Retrace a Line" mean? Absolutely nothing and it should not be words for this problem. It's like saying "connect the dots without picking your nose". Your picking not being part of the problem. Unless the desire is to trick people. But why? Also, there is a solution for connecting 9 dots with one line in highly curved spacetime. Also, perhaps a line extended to infinity wraps around and can be used to complete the diagram. All these lines are locally straight. It does not curve, but space does. If the 9 dots are drawn on paper then by folding the paper, all dots can be aligned above one another and then a single line pierces through the paper will connect all dots. Or you could just say that folding the paper makes the dots come together and require no lines whatsoever. I'm saying that your solutions are very boring. No really thinking outside the box... just solving as expected. Yawn.