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You don't have a tool to measure to the "middle" ... unless you mean wait for 30 min then set light to the other end.
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If it't a rope, you don't need a tool to find the middle. Just fold it, then pull the ends apart a little bit so that it lies in the shape of a V.
The good thing about pessimism is, that you are always either right or pleasently surprised.
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If you read some of the other posts, you'll note that this was disallowed: "Not allowed to fold the rope".
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The only way this can be done with a single rope is either by exact measurement or proportions of the rope. Since you can neither measure it (no tools) nor find proportions (requires bending the rope) this cannot be done accurately.
However, if you have two ropes this may be possible:
Light both ends of one rope and one end of the second. When the first rope is fully burnt light the other end of the second rope.
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Typical bullshit questions.
As for the rope, what are you allowed to do? Are you allowed to fold it in half?
The smilies are even more under-specified. What exactly are the moves you're allowed to use? "Use a combination of (2 + 1)" doesn't mean anything.
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I'm guessing that in the interview it wasn't in English, and it just doesn't translate well.
Those who fail to learn history are doomed to repeat it. --- George Santayana (December 16, 1863 – September 26, 1952)
Those who fail to clear history are doomed to explain it. --- OriginalGriff (February 24, 1959 – ∞)
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It was in hindi, my native language. I am sorry couldnt translate that good.
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Don't worry about it - I figured it was. Translating jokes and puzzles is never easy, because words often have multiple or subtle meanings, which don't translate well.
Those who fail to learn history are doomed to repeat it. --- George Santayana (December 16, 1863 – September 26, 1952)
Those who fail to clear history are doomed to explain it. --- OriginalGriff (February 24, 1959 – ∞)
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Hello Sir,
Please dont be upset with me.
Firstly, It was asked to me. I dint make it up.
Secondly, you cant fold the rope.
Lastly, consider the smilies as balls. You are supposed to move the balls or place the balls.
Combination of (2+1) means either in the first move you pick 2 balls up and then 1 ball or vice versa, your wish.
Thanks,
Rahul
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I blame the interviewer for this, not you.
Ok what are you allowed to do with the rope then? If you can only set it on fire and observe it from there on it'll just burn for an hour with nothing you can do about it.
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Um.
How many ends does a rope have?
Those who fail to learn history are doomed to repeat it. --- George Santayana (December 16, 1863 – September 26, 1952)
Those who fail to clear history are doomed to explain it. --- OriginalGriff (February 24, 1959 – ∞)
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You are nearing the answer OG. I guess you might have figured it out
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That's in violation of my stated assumptions. In order to utilize both sides, you have to be able to light it twice, which means you can do more than just light it and then observe.
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Nah - you just touch the two ends together and light them both at the same time! 
(Or light one end from the other, but that produces a slightly less accurate 1/2 hour)
Those who fail to learn history are doomed to repeat it. --- George Santayana (December 16, 1863 – September 26, 1952)
Those who fail to clear history are doomed to explain it. --- OriginalGriff (February 24, 1959 – ∞)
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You might have found a loophole.
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It's good stuff, this rope theory! Cutting edge...
Those who fail to learn history are doomed to repeat it. --- George Santayana (December 16, 1863 – September 26, 1952)
Those who fail to clear history are doomed to explain it. --- OriginalGriff (February 24, 1959 – ∞)
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In this case no noose is good news
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Light it in the middle.
You'll never get very far if all you do is follow instructions.
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How do you know where that is?
I would have liked to fold it in half, get the middle that way, then fold it again at 3/4 for part 2 of the question, but OP said no folding..
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I'd fold it anyway. The interviewer sounds an ass. The question is likely something that has morphed beyond recognition with retelling.
You'll never get very far if all you do is follow instructions.
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Easy: Burn the interviewer first, then fold the rope. 
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Thanks sir,
well i told him
to measure it for half an hour, burn it from both the sides. He told me, but then nothing of that rope will be left.
I said, as it is even if you cut the rope into half nothing will be left.
He then smiled. Actually i dint understand what was the intention.
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Where's the constraint about not being able to fold the rope?
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I think that's the whole point - they expect you to talk about what do and how that would give the desired result - in other words its a test of your ability to reason and explain your reasoning (like so many of these wanky things).
So you could answer. fold rope in half, cut it and get two half-hour burns (ie light them simultaneously), or - as someone else said - light both ends. For the 45 mins, fold in half, fold one half in half again, then light the bend - the longer piece will burn for 45 mins, and so on.
For the smilies, it's easy to see how to move a group of 3 to swap the figure, does that count as 2+1 or 3 - you would be expected to reason that out.
I prefer to talk to someone generally about their work, get them to meet the team and talk about things they've actually done, including some technical discussion and reasons for why they took the approach they did. Simple reasoning tests like this where there is ambiguity, and where you are expected to reason about the answers have more value than many things done at interview, even though I wouldn't use them myself.
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