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?
Answer
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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