I recently heard this brain teaser, and have been told that there does, in fact, exist a solution:
Draw three boxes in a row, and three circles directly under the boxes. Connect each box to the circle below so the figure somewhat resembles this:
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O O O
Not the best visual representation, but I hope you get the picture. The hash marks are squares, and the lines should join the circle and the box.
Anyhow, the goal is to connect each circle to the other two boxes without crossing lines. The person who asked me this question swears that there is an answer, but he doesn’t remember it.
Supposedly, this has a normal, real solution, and not a trick answer. This has been driving me nuts for a week…Anyone have any ideas?
I’ve run into this one - as I recall, it’s impossible on a plane surface, you need to put your circles and boxes on a three-dimensional shape. Specifically, you need a toroidal (doughnut) shape, but I don’t remember why, and don’t have a diagram handy to explain it.
No. Curved is fine. Any lines are OK. Just try it and you will see that when you get to the last two lines, there’s no way to connect them to the appropriate boxes without crossing another line. At least no way I’ve found.
Steve - I’m coming to the conclusion that it cannot be done in two-dimensional space, regardless of my friend’s assertion that it can. There have been several times I thought I answered this question, only to go back and realize that I’ve connected a circle to the same box twice or connected a box with a box or a circle with a circle.
I’m wondering if other people have come across this, and know for definite that no solution exists on a flat plane.
And are the lines you can’t cross the original ones only( in which case this is a really easy puzzle), or also the ones you are asked to create? If your friend can’t remember the answer, are you sure you have your question right? Sometimes with brainteasers like this, even a little bit of off-wording or wording left out can be the key to the whole mess.
All of these questions of course mean that I couldn’t figure it out either. And I tried Francesca’s suggestion, but you end up crossing lines that way too. Hmmmmmm…
bella–who’s going to be dwelling on this all day
on preview, I see Steve Wright has chimed in with a completely unvisualizable solution. Not that I don’t trust him, but it’s still going to bug me until I have that ‘click’ of comprehension. Gaaahhh!
(Background noise: a small child asking “Mummy, why is that man frowning and writing on a doughnut?”)
I think it’s the last two lines that require the toroid. You can draw all but two in a plane… then the last two have to curve out of the plane, and come back in another direction, so there has to be a hole they can come back through … I think I have just sprained my frontal lobes trying to visualize this…
Belladonna - yes, you are interpreting the problem correctly. This is how it was presented to me, and my friend claims not to have left out or misremembered anything. I’ve asked the same questions you have asked, and I’m representing the problem accurately. Now whether HE’S representing the problem accurately, that’s another story. As I said, he swears there’s no trick, no word-play, no gimmick to the solution. Just a bunch of curvy lines.
He says he saw the problem solved himself and he says he once did it himself and forgot the solution. Anyhow, he’s not prone to lying about these sorts of things just to drive me nuts. I have a feeling that he probably DID think he saw a correct solution, but upon further inspection was wrong.
But I can’t tell him there is no solution just because I couldn’t find one. Maybe there is. I don’t know.
Steve- Yeah, basically that’s right, but I don’t see the point of this teaser if in fact that is the answer.
No, this is not some great thought in leet form. This is simply what happens when you try posting with your 9 month old on your lap. Mods–a bit of a cleanup please? ::batting eyelashes::
Meanwhile, I’m getting more what Steve’s saying, but still really hate it when puzzles have overly complex solutions. I’m just going to pretend it has a “conventional” answer and keep obsessing over it, kay?
Can you put the lines through the circles and squares? That is, draw a line through the circles, curve it up in a 180° arc and run it through the squares, then make another 180° arc so that the line rejoins itself in the first circle.
Think of it like a string of Chrismas lights. The old kind where if one bulb is bad, none of the lights will work. A single line goes through each shape (“bulb”) without crossing itself. Thus, the line connects each circle with all of the other circles and all of the squares.
(Hey, there was nothing in the rules that said you couldn’t go through the shapes or join them all together!)
I don’t think there is a solution to this in 2-dimensional space.
Since the lines connecting the circles and squares can be moved and stretched (just not broken), the initial location of them on the paper is irrelevant. So, place the items in the shape of a circle - alternating circle and square (i.e. circle at 12 o’clock, square at 2 o’clock, circle at 4, square at 6, circle at 8, square at 10.)
Connect the circles to the squares to complete the “big circle”. Ok, now each square needs to be connected to the circle across the “big circle”. Connect one pair as the diameter of the “big circle”. When you connect another pair outside of the “big circle”, you have “isolated” one half of the last pair and there is no way to make the connection on paper.
My dad presented this problem to me years ago, with the same claim that he’d seen the solution. At first he wouldn’t tell me, many years later he couldn’t remember. I doubt the solution exists.
Philster, I don’t see where going around the tube presents any option that isn’t available from simply making an end run around everything on a flat sheet.
That’s what I was thinking. Brain “Teasers” always have some stupid solution like that. They phrase the question in such a way that you think it’s one way. For example, they say “on a sheet of paper”. They don’t say anything about not rolling the paper, or having to create a 2D figure only.
The original question to this was probably “on a sheet of paper”, thus rolling the paper into a cylinder is the correct answer.
Watson has Homes solve this problem in Doyle’s A Study in Scarlet. The solution Doyle gives requires a threedimensional surface, and it is explicitly said the thing is not solvable on twodimensional ones.
I remember seeing this problem when I was ten, except it was in the pretext of laying utility pipes from three utilities to three homes. And the solution required breaking 2D space, specifically by having some pipes lie over/under each other.
As stated above, the problem is usually stated as providing three utilities (water, gas, electric) to three houses without having any of the lines crossing.
Here is my solution.
The three circles are the utilities and will be represented by:
w (water)
g (gas)
e (electric)
My solution is to locate one of utilities in each house. So each house provides one of the three utilities itself. In terms of the OP, just put each of the circles inside the three boxes and then connect the circle to its own box internally and the other two via external connections.
Ok, that’s ugly, but you can draw it for yourself very easily. I didn’t draw the internal connections between each box and its own utility, but you can see that can be done easily without crossing any lines.