Solutions to Two Puzzlers About Drawing Lines

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.

Thank you

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

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.

Oh pipe puzzle!!! I love those.

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.

Fun

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

The big box is the thumnail

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.

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.

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

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

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

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.

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

DeathSatan would call that CRT indoctrination.

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.

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

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

I did it without picking up my pencil

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.

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

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.

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

too easy did in first try 5 seconds!

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

Happy with myself that I figured out the second one

Managed to solve 1st puzzle inside of a minute.

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.

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.

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.

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.

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!

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)

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.

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.

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

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

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

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

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

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

"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.

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.

The answer is: Impossible

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?

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

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