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All the rooms in this hotel correspond to


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Since it's tagged 'lateral-thinking', an alternative that blatantly ignores the question's title is that:


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The introductory paragraph is a clue to As Arnaud has pointed out


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He entered


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The answer is: As: Resulting in:


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I can't see any pattern in the given list of zeroes, so maybe the answer is That would be because the paper being imaginary suggests that and then the line underneath the zeroes suggests With this in mind, we can split the zeroes into groups of three lines, which happens to be (No. That's not at all far fetched! Why do you keep saying that? Well, maybe ...


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Reasoning


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Based on DEEM’s hint, the answer is I think this is because


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Oops, looks like you So it should look like this: Which means the message is:


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By using we can obtain


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I think this could be an answer:


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The mathematical (a.k.a. obvious) solution: The lateral-thinking solution:


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The day had been ... Why?


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Answer:


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The wrong book is because


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The description of "5/8 of the way into [your] meal" could imply that you are: This particular establishment: This means that among the clientele would be: The shoe-less customer could therefore be: (Similarities with SteveV's answer perhaps but hopefully you can also see the differences and the justification...)


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It's additive therefore,


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Possible solution: Possible Lateral Thinking answer:


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I think the answer might be What can you take but not give? What takes hours to do but it’s over in an instant. You can get it but never save it. What gives you sight without seeing? Run without legs. Travel the world but never leave. The past is now. The future is history. We all have been there. It’s free. You can do it with family and friends but ...


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Well, first I have to solve the math problem, I guess.


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Here's one possible solution: Q.E.D.


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They are


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I think the middle number is First sequence Second sequence Third sequence


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Easy math:


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