The Five Square Puzzle

[Universezero]

Recently my cousin gave me a maths puzzle to complete. It's intensely hard... the goal is to draw a continuous line that goes through each side of the squares each line segment only once.



The left shows every line segment you have to pass through. Here are a few attempts so you get the idea:



Those are obviously failed ones, as I missed a couple of sides. Apparently it took my cousin years to solve; he had to be shown the "secret". I'm hoping one of you already knows it.

Note: This puzzle is NOT this one. The one here has much more line segments, is much harder, and I can't find it anywhere else on the web.

[otters~1]

People thought there was a secret to this one, too.


EDIT: When I typed "The bridges of konigsberg" into Google, the first auto-complete that showed up, naturally, led to this thoroughly excellent map, which I had forgotten until today.

[Universezero]

People thought there was a secret to this one, too.

I have been told this one is possible to solve, however. My cousin did give me this clue for me and to post:

"In order to solve the problem, you need to not think in straight lines; in fact, you'll need to think outside the box."

He then corrected himself and said, "Actually, say 'think outside the square,' but I don't know if that's of any consequence.

[SlappyMcGee]

People thought there was a secret to this one, too.


EDIT: When I typed "The bridges of konigsberg" into Google, the first auto-complete that showed up, naturally, led to this thoroughly excellent map, which I had forgotten until today.

I loved that map! I played it a thousand times before googling "Konigsberg is retardo."

[scythe]

Sorry, but this is provably impossible. The puzzle can be quite easily transformed into the equivalent graph: each square, plus the outer region, is a node. Each line segment is represented by an edge on the graph.

The resulting graph, which is equivalent to the original puzzle, looks like this:



The number of edges leading from each node is 5, 5, 5, 5, 5, and 11. There are six nodes with an odd number of edges; however, it is only possible to find an Euler path on a graph with two or zero such nodes. Therefore, the puzzle has no solution.

Note also that any solvable puzzle of this nature may be solved algorithmically; that is to say, it's hardly a puzzle at all.

EDIT: Also, if you don't have to pass through half-segments as though they are distinct, Amadeus's solution is correct. My post regards the other case, which is apparently the one which you were trying to solve.

[Amadeus]

Just draw a straight line diagonally down crossing through the boxes and loop around, like this:

EDIT: Oh line segments, yeah I agree with scythe I don't think that's possible. Are you sure he didn't mean sides because that makes a lot more sense.

[Universezero]

Ugh, he told me the answer. It's essentially impossible without going into non-Euclidean geometry. Sorry for making you all waste your time.

[Scrivener]

I'm pretty sure that means you'd have to use the 3rd dimension which makes it a pretty stupid solution to an otherwise impossible puzzle.

[t̷s͢uk̕a͡t͜ư]

And computer science mercilessly crushes yet another "challenging" puzzle. Good job, scythe.

It's essentially impossible without going into non-Euclidean geometry.

Did you see scythe's graph diagram? We were already using non-Euclidean geometry, lol.

[Universezero]

He showed me this on a piece of paper. He punched a hole in the paper with the pen, then drew the line on the other side of the paper, thus not going over any lines, but allowing him to bypass ones he had. When I found out, I was fairly disappointed that it wasn't logically solvable.

[OneSevenNine]

I believe this is relevant.



There's clever, and then there's deliberately breaking the implied rules of your own game.

[scythe]

I believe this is relevant.



There's clever, and then there's deliberately breaking the implied rules of your own game.

So much for "warmongry".

[Rose]

I believe this is relevant.



There's clever, and then there's deliberately breaking the implied rules of your own game.

I don't even get it >_>

[Universezero]

I believe this is relevant.
There's clever, and then there's deliberately breaking the implied rules of your own game.

I don't even get it >_>

There are three words in the phrase "The English Language", the third of which is the word "Language".

[Rose]

I believe this is relevant.
There's clever, and then there's deliberately breaking the implied rules of your own game.

I don't even get it >_>

There are three words in the phrase "The English Language", the third of which is the word "Language".

"that end in 'gry'." I just can't see how, with that added on, you can add language to that :s