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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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    $\begingroup$ 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. $\endgroup$ Nov 11, 2014 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". $\endgroup$ Nov 11, 2014 at 9:50
  • $\begingroup$ Maybe I should self-answer this. $\endgroup$
    – warspyking
    Nov 11, 2014 at 15:35
  • $\begingroup$ are you sure the answer for 1 is 1 ? not 2 ? $\endgroup$
    – njzk2
    Nov 11, 2014 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, 2014 at 16:20

2 Answers 2

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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, 2014 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, 2014 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, 2014 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, 2014 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, 2014 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, 2014 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, 2014 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, 2014 at 4:02

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