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All the rooms in this hotel correspond to


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


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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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He entered


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The answer is: As: Resulting in:


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You could EDIT:


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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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Your favorite letter is And it appears


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Since: So, first: Then: While simultaneously: And:


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


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It will be Both A and B can see, what C sees, and that's why they both know that From there, the problem reverts to the earlier one:


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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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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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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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The wrong book is because


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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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Easy math:


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