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After not getting invited to any of the parties that have been going on lately I decided to make my own. As expected I hired my own security guards and sent out a letter to all the invited guests with instructions on how to answer the guards when told a random number. Of course the likes of you would not be invited but you decide to try and decipher the "code" needed to get inside. You lay in wait and hear a couple of people who actually were invited and what their responses were. It Went as follows

The first guest arrives and the guard says "13". the guest says "5" and the guard steps aside and lets the guest inside.

The second guest arrives and the guard says "23" and the second guest says "7" and gets let inside.

The third guest arrives and the guard says "17". the third guest answers "6" and goes inside.

The fourth guest arrives and the guard says "19". the fourth guest says "4" and gets KILLED RIGHT THEN AND THERE.

You feel confident that you have cracked the system and decide to give it a go. You walk up to the guard with a smug on your face and the guard goes "33". What do you say in order to get in to the party and not killed.

(please put your answers in spoiler tags)

NOTE: The answers are not the results of a mathematical function even though such a function most likely does exist.

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  • $\begingroup$ Yes that might be true. i just didn't look through them properly. im lazy $\endgroup$
    – Legotruck
    Commented Nov 17, 2014 at 10:00

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Is it

the number of lines in the Roman-numeral representation of the number the guard gives?

That matches all the questions and answers you've provided, and the right response to '33' is

9

while the right response to '19' was

5.

(This idea was used in another of the 'Security to the Party' questions, but I can't remember which one! +1 for new formatting of the question anyway.)

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    $\begingroup$ Well done :) i knew this wouldnt take long to crack $\endgroup$
    – Legotruck
    Commented Nov 17, 2014 at 9:54
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The small number of examples dont do justice to such questions. The purpose of this answer is not to "answer" the question but just to show that its easy to come up with some function that fits

Rounded up value of $(((x-3)/5)+3)$ i.e (((13-3)/5)+3) = 5, (((17-3)/5)+3)=5.8 rounded up to 6

So going by the above logic your answer should be 9 (((33-3)/5+3)

Please don't place spoilers for this, I mean it to be open.

This answer was made prior to the clarification, so before downvoting take that fact into consideration, I am leaving it here as proof and guideline, I am not worried about negative reputation from here but feel it does not deserve to be downvoted or upvoted

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    $\begingroup$ That is probably true but i can say that for this one i didnt mean for it to be the result of a mathematical function. its a more straight forward reasoning. ill add it to the question. $\endgroup$
    – Legotruck
    Commented Nov 17, 2014 at 9:26
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    $\begingroup$ I find it to be very rare that the puzzle poster ever intended for their solution to be a simple mathematical function. If I were to post another one of these questions, I would attach the stipulation that it should be a calculation one could do mentally. $\endgroup$
    – Psychemaster
    Commented Nov 17, 2014 at 9:48
  • $\begingroup$ a mathematical function was indeed NOT intended as the solution to this problem. i added this at the end of the question $\endgroup$
    – Legotruck
    Commented Nov 17, 2014 at 9:52

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