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This puzzle is pretty easy but sure and entertaining one. so take your pencil and start matching the columns. don't look into another answer to enjoy it.

well, what you need to do is to draw a line from each block example x to the other block x. you need to match all the blocks v, x, y, and z.

rules:
1. no line should overlap each other.
2. no line should go outside the boundary.

enter image description here

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4 Answers 4

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This is pretty fun indeed! :)

enter image description here

Don't forget to read @trolley813's concise proof (and upvote it :P)

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    $\begingroup$ Very nice! Perhaps it'd be worth linking to the proof from @trolley813 that this answer is indeed unique? $\endgroup$
    – Brandon_J
    Oct 3, 2019 at 13:25
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Took another approach...

straight lines only my Solution

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    $\begingroup$ Bonus points for completely understanding the difference between "Rules as written" and "rules as intended". You rules-lawyer. $\endgroup$
    – Gloweye
    Oct 4, 2019 at 11:22
  • $\begingroup$ I asked this question to the 5th class grade student and he gave me this answer :P. $\endgroup$
    – Sayed Mohd Ali
    Oct 17, 2019 at 13:11
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Well, not strictly an answer (since I've found exactly the same as one already posted), but rather a proof that other ways are not possible:

The lower X block lies on the boundary, without any margin (and the upper X block does so), so the X-X line will divide the whole sheet into 2 disconnected regions (since the X-X line cannot be bypassed). It's now clear that the central V block must be in one of these regions, while the central Y and Z will be in the other. So, the only challenge is to draw the X-X line keeping both Vs on the one side of it, and all other letters (Ys and Zs) on the other side. The only way to draw it is shown by @OmegaKrypton in his answer.

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    $\begingroup$ There are two ways of drawing YY and ZZ. Imagine YZYZ is a boundary, then it creates an 'inside' and an 'outside', and only one line can be in each partition. OK has YY on the inside of YZYZ, but ZZ could be on the inside for a different solution. $\endgroup$
    – JMP
    Oct 3, 2019 at 16:08
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    $\begingroup$ There is a second way to solve it, though to be fair it does keep the Vs on the "opposite side" of the Ys and Zs. I think it's effectively the mirror image of the other answer. $\endgroup$
    – Rob Watts
    Oct 3, 2019 at 20:29
  • $\begingroup$ Nice explanation. $\endgroup$
    – Sayed Mohd Ali
    Oct 4, 2019 at 6:16
  • $\begingroup$ There are infinitely many different ways to solve this puzzle. Imagine drawing the solution on cappucino foam, where the floating v,y,z blocks are spoons. Now you can move the three spoons around each other, changing the paths without making the solution invalid. For mathematicians: The set of solutions (mod relative homotopy) has a free and transitive action by the (infinite) pure braid group P3. $\endgroup$
    – Magma
    Oct 4, 2019 at 9:44
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I found a different way to solve it.

Solution

Note that this doesn't disprove @trolley813's proof - it only shows one part of the proof is incorrect:

"So, the only challenge is to draw the X-X line keeping both Vs on the one side of it, and all other letters (Ys and Zs) on the other side. The only way to draw it is shown by @OmegaKrypton in his answer." - I believe that my answer is the mirror image of @OmegaKrypton's, so if you are considering this problem as a graph it is actually the same. It is also easy to loop the lines around z and y as many times as you want to produce images that look different but are based on the same graph: Same yet different

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