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A party is being held at a local mansion. The host is very rich and his success is because of one thing ~ his famous recipe for Spaghetti!

The only guests that may attend are people the host knows and trusts, whom he gave the password to enter to.

Here's where you come in. You and a friend are trying to steal this recipe. You sneak by and listen to the passwords.

The first guest arrives. The security says "5", and the guest replies "5".

The second guest arrives. The security says "6", the guest replies "6".

Your friend thinks he got it all figured out. He approaches the security and as they say "7", when he replies "7" he's taken by security to the host for impersonating a guest.

Another guest arrives, you seem to get the same pattern, security says "1" and he says "1" to get in.

The final guest before you figure it out comes and says "4" in which the response is (you guessed it!) "4".

You walk up to security and get "3", what is the correct response?

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closed as primarily opinion-based by skv, Kenshin, Peter Taylor, Rob Watts, Rafe Nov 12 '14 at 18:38

Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ I am downvoting this question on the basis you are evaluating answers based on whether they match what you had in mind, rather than whether they work based on the information provided. I consider questions where the puzzle author is doing this to be unhealthy for the site, so I am voting accordingly. $\endgroup$ – doppelgreener Nov 11 '14 at 7:52
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    $\begingroup$ how exactly is that a valid puzzle? given the information provided, the correct answer could be anything, be it "42", "bananas" or "punch the guard in the face". $\endgroup$ – Jeor Mattan Nov 11 '14 at 9:50
  • $\begingroup$ Maybe I should self-answer this. $\endgroup$ – warspyking Nov 11 '14 at 15:35
  • $\begingroup$ are you sure the answer for 1 is 1 ? not 2 ? $\endgroup$ – njzk2 Nov 11 '14 at 16:18
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    $\begingroup$ @njzk2 The hint seems to imply it might be; but it will make it the same puzzle as [part2] $\endgroup$ – Kami Nov 11 '14 at 16:20
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There are many possible answers. But I will say...

The answer is:

In general, the last digit of $x^3$.
$$\begin{align}5^3 &= 125 \\ 6^3 &= 216 \\ 4^3 &= 64 \\ 7^3 &= 343 \\ 3^3 &= 27 \end{align}$$

From this, it is clear that we should respond:

7 (as response to 3)

Our friend should have answered:

3 (as response to 7)

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    $\begingroup$ +1 I think this is what he was looking for because on my part 2 his first guess was 3. $\endgroup$ – Kenshin Nov 11 '14 at 5:48
  • $\begingroup$ @skv True, well done you. I guess there's no actual reason from our perspective why one should be correct over another :p $\endgroup$ – d'alar'cop Nov 11 '14 at 7:54
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    $\begingroup$ @warspyking this is a very well thought out answer, why dont you accept this, or add other numbers that will prove this wrong $\endgroup$ – skv Nov 11 '14 at 17:31
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The formula is:

$x \mod 7$

So the answer you should give is:

$3$

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  • $\begingroup$ Sorry but this is incorrect. $\endgroup$ – warspyking Nov 11 '14 at 2:58
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    $\begingroup$ @warspyking How is it incorrect? It satisfies all the information provided in the question. I think what you meant to say there was "Sorry, that's not the answer I'm looking for." I get that you're looking for a specific answer, but for a question with as many possible answers as this one has 'incorrect' seems entirely unfair. $\endgroup$ – Miniman Nov 11 '14 at 3:01
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    $\begingroup$ @Miniman exactly the point of this answer, I am not proud of it either, but its so open ended that people can come up with more than one "correct" answer $\endgroup$ – skv Nov 11 '14 at 3:04
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    $\begingroup$ Okay let me rephrase that @Miniman this does fit the other passwords however it is not the system the host used. Good try, feel free to try again :D $\endgroup$ – warspyking Nov 11 '14 at 3:07
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    $\begingroup$ I was considering giving this answer. Only thing I could come up with that fits. $\endgroup$ – Mr.Mindor Nov 11 '14 at 4:02
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Easy. :)

You said that the only guests that may attend are people the host knows and trusts. As he doesn't know neither my friend nor I, we can't get in to steal his recipe!

In this case, the passwords are useless, and there is no good answer.

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    $\begingroup$ No, the password is to distinguish between guests and impersonators. $\endgroup$ – warspyking Nov 11 '14 at 2:57
  • $\begingroup$ Well. You did say "whom he gave the password to enter to.". Nowhere says my friend and I received the password from him, so he knows he did not give it to us. ;) $\endgroup$ – marcantoinefortier Nov 11 '14 at 3:01
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    $\begingroup$ The security has no idea whom the host trusts. This is the point of the password, do the host don't have to greet a bunch of imposters. $\endgroup$ – warspyking Nov 11 '14 at 3:05

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