# The Security to the Afterparty

So, you got through the guards and to the party? Easy stuff! The number sequences were silly and you walked in and out multiple times. Now what? One of the guests you mingled with at the party has told you about an afterparty in the works. The location, the staff, the people invited - you know all the details.

In a classy outfit you slide into the mansion where the afterparty shall take place at. The two guards are thick and dense as logs, but brighter than most folk you've met. Behind those classy glasses sits dry wit.

You come with three more chaps and a pair of gals you met at the main show. You joke around a bit and line up to get in.

The first is the ginger guy who's as pale as vanilla. He comes up to the guards and says: "Tell me." The left guard says "zero point 940542104683244" and the right one goes "minus 12340633 over 36330480." Stunned at the sequence, you quickly tune in on the proceedings. The lad gives it a couple seconds' worth of thought and says: "Two." They let him pass.

Second goes the black woman. She eyes the guards for a moment and then says: "Hit me." The left guard goes "zero point 955741461871332" and the right one goes "minus 13047101 over 44346543." She metaphorically chews it over and says: "Six, should be." She gets through as well.

Third is the average Joe who came to the party to meet women, not eat spaghetti. The left guard goes "one," but the right one says: "Nothing from me." He starts panicking visibly before he stutters out a meek "Zero?" The guards shake their heads and he walks away, defeated.

Fourth is the blond guy you've seen sip far too much champaigne. The left guard tells him: "You get a zero point 948639957057241" and the right one goes "minus 18032031 over 56998858." He blinks at them a couple of times, then cups his chin for half a dozen seconds. "Five?" The guards nod and let him pass.

Fifth is the short, burly brunette. The left guard tells her "zero point 6532814824381882" and the right one goes "minus 17280845 over 63861676". She lets out a bored "imaginary four" and ploughs her way through the guards.

You are stunned by the sheer brainpower of the people you drank with. Your turn now. You gulp and look at the smiling men. The left one says: "So, for you... zero point 933581447902683?" The right one nods and goes "minus 17753215 over 49539438." You're looked at expectantly. The brunette's waiting on you behind the duo. What do you say?

Hint 1:

The right guard always says a negative number. Why is this so?

I have no idea how to work backwards on this, and I don't know how #5 works so maybe someone else can pitch in. But anyway...

2.5

Reasoning:

1.

"zero point 940542104683244" and the right one goes "minus 12340633 over 36330480." ... 12340633/36330480 = .3396771251 ... 0.940542105 + 0.339677125 i = 2^(i/2) so 2.

2.

"zero point 955741461871332" and the right one goes "minus 13047101 over 44346543." ... 13047101/44346543 = 0.2942078484 ... 0.955741462 + 0.294207848 i = 6^(i/6) so 6.

4.

"zero point 948639957057241" and the right one goes "minus 18032031 over 56998858." ... 18032031/56998858 = 0.3163577593 .... 0.948639957 + 0.316357759 i = 5^(i/5) so 5.

6(you)

"zero point 933581447902683?" The right one nods and goes "minus 17753215 over 49539438." .... 17753215/49539438 = 0.35836528868 ..... 0.933581448 + 0.358365289 i = 2.5^(i/2.5) so 2.5

• While your solution is the one (congrats!) the means that got you there are almost correct! Note that there's a "minus" with every number that Right gives. If you want a hint, feel free to ask. But yeah, congrats on getting in! There's cake and freshly delivered pizza! – Darkgamma Nov 11 '14 at 23:44
• @Darkgamma I'm disappointed nobody else gave it a shot. :( I'm interested in what the right way to solve this is though, especially since my way was pure guess&check once I discovered the pattern in the first few – DHall Nov 17 '14 at 18:24
• Hey, not everyone can do advanced maths! The fundamental difference is that I went with n = x^(-i/x) (different sign of the exponent!) and for 2 that gives 0.940542... - 0.339677... i and 4i gives 0.653281 - 0.270598 i. A sign shift, yeah, but kinda an important one at that. You did get the correct result (six) by adjusting the signs. Wasn't 100% on mark but good work anyhow! – Darkgamma Nov 17 '14 at 18:35