Evil Kidnappers are the worst!

Question

You wake up to the sight of a lamp hanging from a grey ceiling. You ask yourself, Where am I? The last thing you remember is falling asleep in bed last night. Sitting up, you look around. You're on the bed in some sort of prison cell, and there's a crumpled note beside your feet.

Let's see if you can get out of this one. You've caused me trouble for the last time!

- Evil Kidnapper

P.S: Stop telling people I don't recycle and I'll stop doing this to you.

You think to yourself, Oh, it's the crazed freak that's obsessed with puzzles again... Flipping the note over, you notice that it's the label from a bottle of pop of some sort. It's missing a few parts though...

____________________________
|Nutrition facts           |
|Per 355 mL                |
|Calories                  |
|Fat 0 g                   |
|Sodium 15 mg              |
|Carbohydrate 42 g         |
|   Sugars 41 g            |
|Protein 0 g               |
|                          |
|CAFFIENE CONTENT          |
|   mg/355 mL              |
----------------------------

As you get up and walk around the room to take a look around, you notice that there's a keypad that's hooked up to a door. Clearly, if you put in the correct code the door will open and you'll be able to escape.

You start walking towards the keypad, but you almost slip on another sheet of paper. It's separated into several sections, and you give it a read.

Nothing is more important to me,
than the bonds of my family.
Each piece below is a key from them to thee,
spend some time and you just might get free.

I'm all natural, all the time -
Euler used me but I feel fine.
I'm the find in many ways,
a unique treasure who likes Swiss cheese.

Irrelevant information influences influential individuals.
I infrequently integrate idioms in ideas.

You get rid of me several times a day,
but I'll come back after a slight delay.
Those bound to earth already see,
should you ever stop relieving me,
It's a sign you've been released.

I'm always moving,
with no need to stop.
I've no place to be going,
but it doesn't matter - I'm first!

I'd tell you who I am if you could catch me,
but I'd slither away before you could see me.

To summarize: My first brother is always the same, the next is narcissistic.
Another brother moves like a river, but his twin is impossible.
My sister can be quite quiet, but when she's angry you don't want to hear her hiss.

P.S: I've left you a trace of my family. Good luck - Evil Kidnapper Minion (A big fan)

Well that's mighty helpful, you say. As you further examine the room, you notice that there's an inscription on the floor.

$$\mbox{___} \times \mbox{___} - \mbox{___} + \mbox{___} = 398$$

A grin spreads across your face as it dawns on you. Huh. I think I've got everything I need.

Your task: Figure out the code and escape.

(Hints below)

3 Hours later

Scratching your head furiously, you scream Aaagh! It's not working! Why doesn't it work? Did I miss something? You go over all the clues and items in the room again and find that you've missed some fine print under equation.

If I were a box shaped animal I'd be missing most of my hide. Find your family and scramble the eggs to find the missing sides.

Another look at the riddle sheet shows that another kind minion has left you a hint.

The family tree has 27 people. If you include yourself, then your immediate family consists of 6 people. The "bonds of my family" only count your immediate family!

Another hour later

Continuing to ponder, you scratch your head. Hm... this is harder than I thought it'd be. I'm pretty sure the bonds have nothing to do with the periodic table though.... Which means it has to have a hidden meaning! But what could it be?

2 hours later

I've deduced that I, as a person, am definitely extremely different than those in my family. Your stomach grumbles with hunger as you sit down and try to figure out the rest of the problem...

Another hour later

Hmm... Definitely nothing to do with Astrology... you grumble, sitting on the cold cell floor.

One Day Later

You think to yourself, How am I not out of this mess already? Frustrated, you bash your head against the wall. Eureka! There are exactly three parts to this puzzle! I'm pretty sure the riddles get me letters that help me get the missing numbers on the label, which would help me solve the equation! Now if only I could actually complete the riddles...

Answer 1

The Answer is:

8 x 50 + 1 - 3 = 398

The reason is:

As has already been stated, the Nutritional Information matches that of a Pepsi can. PEPSI has five letters. The Calories are 150 while the Caffeine Content is 38. I say these five numbers correlate with the five letters in PEPSI. I know there are four slots used in the equation to get 398, so I think that (as the hint says) solving the riddles will give me the answer. I therefore think that by corresponding each letter with one number, the answers the riddles give me will provide the answer: P=1 E=5 P=0 S=3 I=8 The first paragraphs talks about a Swiss cheese afficionado, and seeing as it's to do with Euler I'm going to say it was talking about Euler's number i.e. E. The second paragraph talks about a self-interested 'figure' who appears in idioms (easy as pie), so I think it's Pi. The first letter of which being P. The third paragraph references something which moves like a river. I would see this as something forever continuing, therefore Prime, i.e. the letter P. To further support this answer the riddle in this paragraph states it is gotten rid of "several times a day". If you were to look at Prime in relation to the Seven Canonical Hours it is the first hour of prayer in the day and comes to be at around 6AM. Seeing as there are two 6 o' clocks in the day I would say Prime fits the answer for this paragraph. The fourth paragraph is a twin (further supporting the idea that Paragraph 3 is Prime i.e. twin primes) and "impossible". Therefore the letter: I. The fifth paragraph talks about a figure who 'hisses'. I'd call this Sigma based on theories of the Greek word beign based on a nominalization of a verb σίζω (síz��, from earlier *sig-jō, meaning 'I hiss'). Putting the letters in order they spell: EPPIS Imagine the string is repeated immediately after itself: EEPISEEPIS I think that by taking the first letter and jumping forward to spaces, and then again, and again, and again, you get the desired order: EPIPS. With this order, substitute the numerical values given to each letter: 85013. Substitute into the equation and you get 398.

Thoughts?

Answer 2

It's been 19 days since the trapping. Unfortunately, you are now dead.

Starting with decoding the hints:

If I were a box shaped animal I'd be missing most of my hide. Find your family and scramble the eggs to find the missing sides.

The equation has 4 missing sections in the form of 4 lines - 4 lines can be made into a box. It's also missing all 4 numbers, eg: most of my hide. Finding your family refers to some sort of "family", and scrambling the eggs to find the missing sides means that if you scramble the eggs, you'll get the missing numbers (missing sides, missing hide). By that logic, the eggs are letters, and the scrambling them will somehow gives you the eggs.

The family tree has 27 people. If you include yourself, then your immediate family consists of 6 people. The "bonds of my family" only count your immediate family!

You are a human. There are 26 letters in the alphabet. 26 + you = 27. By the same logic, if you remove yourself from the immediate family, then you have 5 left. Bonds of my family is a reference to the riddle, and this is supposed to tell you that you're looking for a total of 5 letters.

Continuing to ponder, you scratch your head. Hm... this is harder than I thought it'd be. I'm pretty sure the bonds have nothing to do with the periodic table though.... Which means it has to have a hidden meaning! But what could it be?

Self explanatory. Simply states that the puzzle has nothing to do with the periodic table.

I've deduced that I, as a person, am definitely extremely different than those in my family. Your stomach grumbles with hunger as you sit down and try to figure out the rest of the problem...

Used to help decode the earlier hint regarding 27 and 6. If you haven't figured out that you're supposed to subtract 1, this is the hint to do it.

Hmm... Definitely nothing to do with Astrology... you grumble, sitting on the cold cell floor.

Also self explanatory.

You think to yourself, How am I not out of this mess already? Frustrated, you bash your head against the wall. Eureka! There are exactly three parts to this puzzle! I'm pretty sure the riddles get me letters that help me get the missing numbers on the label, which would help me solve the equation! Now if only I could actually complete the riddles...

This is also self explanatory. Simply put: Solve the riddle to get letters to find the missing numbers on the label, to solve the equation.

Solving the riddle:

Nothing is more important to me, than the bonds of my family. Each piece below is a key from them to thee, spend some time and you just might get free.

First 2 lines show that there is some sort of relation coming up (Bonds and family). Each piece below is a reference the the paragraphs below, and the last line is flavor.

I'm all natural, all the time - Euler used me but I feel fine. I'm the find in many ways, a unique treasure who likes Swiss cheese.

"E" - Used in Ln (Log base e, AKA Natural log - it's also a constant, hence "all the time"). Euler used the constant. Also, Euler was Swiss.

Irrelevant information influences influential individuals. I infrequently integrate idioms in ideas.

"I" - Look at all the I's. Just look at them.

You get rid of me several times a day, but I'll come back after a slight delay. Those bound to earth already see, should you ever stop relieving me, It's a sign you've been released.

"P" - "Those bound to earth" are living people. Living people have to go pee! Several times a day! And they always have to go again eventually! Dead people don't pee, however, so "those who stop relieving [themselves of pee]" have been "released" (opposite of bound).

I'm always moving, with no need to stop. I've no place to be going, but it doesn't matter - I'm first!

"P" - Always moving, doesn't stop = perpetual motion. "I'm first" designates the first letter of "Perpetual motion". Note: this is a weak deduction.

I'd tell you who I am if you could catch me, but I'd slither away before you could see me.

"S" - "Tell you who I am if you could catch me" is someone who is sneaky. Slither away references a snake. Note: this is a weak deduction.

To summarize: My first brother is always the same, the next is narcissistic. Another brother moves like a river, but his twin is impossible. My sister can be quite quiet, but when she's angry you don't want to hear her hiss.

The summary helps to confirm the letters. First brother is always the same - Eulers constant. Next brother is narcissistic - all about "I". Third brother (the first "P") moves like a river (Pee is a liquid and it moves like water/river). Perpetual motion is impossible, and it's a twin because both those paragraphs have the answer of "P". Sister being quite is a reference to "shhhh", and the hissing also consists of an "S" sound.

P.S: I've left you a trace of my family. Good luck - Evil Kidnapper Minion (A big fan)

Trace of my family is the label.

Step 2: The missing values on the label

The label doesn't have a brand or anything on it, but you now have the letters E,I,P,P,and S. If you "Scramble the eggs" (Anagram alert), you'll see that you can spell a popular pop brand, Pepsi, with the letters. Googling "Pepsi 355ml nutritional facts" will get you the missing numbers, 150 and 38.

Using those values to solve the equation, you get:

8 x 50 + 1 - 3 or 50 x 8 + 1 - 3 (Both of which are valid codes to open the door).

Note:

It's been pointed out to me that the hint with the 27 and 6 may have been too confusing and resulted in puzzlers being stuck on the hint. I apologize if that caused you to be stuck in any way/shape/form. I'll work on my hint giving skills.

Answer 3

Work in progress.

Paragraph 1: Natural numbers used by Euler: Euler's number, about 2.71828, more specifically, the limit of (1 + (1/n))^n as n approaches infinity.

Paragraph 2: Someone's been watching too much V for Vendetta... Too many words begin with the letter i, which is the square root of -1.

Paragraph 3: Oblique reference to gravity, about 9.8 kilometers per second squared.

Paragraph 4: Neverending, yet looping animation: such is the dance of the planets, but that's stretching it.

Eigenv... nah, that's not going to work much.

Sibling one:

Sibling two: e, a unique number that neatly slips between all other fractions.

Sibling three: g, the gravitational constant that determines river flow.

Sibling four: i, an impossible number.

The sister: A snake...?

Answer 4

To help the others out, I will add my own two cents.

Nothing is more important to me, than the bonds of my family. Each piece below is a key from them to thee, spend some time and you just might get free.

I see this as a strong hint to chemistry. I would guess for a link to fatty acids (fat), as they can be saturated or unsaturated, depending on the type of bonds between their carbon atoms. EDIT: I just realised, if I am sodium, then each of the parts below could stand for a molecule which includes sodium or the element in that molecule which is bonded with sodium.

I'm all natural, all the time - Euler used me but I feel fine. I'm the find in many ways, a unique treasure who likes Swiss cheese.

Eulers number, as Nefer007 said. EDIT: It might be table salt we are talking about here. Still, Eulers number might be important in the calculation. And I would keep chlorine in mind.

Irrelevant information influences influential individuals. I infrequently integrate idioms in ideas.

Again, as Nefer007 said, i EDIT: The I in the periodic table is iodine.

You get rid of me several times a day, but I'll come back after a slight delay. Those bound to earth already see, should you ever stop relieving me, It's a sign you've been released.

This relates to breathing, where you get rid of CO2 (and this is maybe a link to the carbohydrates?) If you stop breathing... you could be seen as released. EDIT: still, carbon.

I'm always moving, with no need to stop. I've no place to be going, but it doesn't matter - I'm first!

Again, I am thinking of elements instantly. The first element would be hydrogen, so we are again hinting at carbohydrates. Maybe we need to look at the number attached to carbohydrates separately (carbon:4, hydrates:2)?

I'd tell you who I am if you could catch me, but I'd slither away before you could see me.

That could be any element which has a short half-life.

To summarize: My first brother is always the same, the next is narcissistic. Another brother moves like a river, but his twin is impossible. My sister can be quite quiet, but when she's angry you don't want to hear her hiss.

I have no idea, but then I would again try looking for elements. Especially a family of elements which has 27 members (no idea), which a sub-family in it that has 6 (alkali-metals or noble gases). Sodium is an alkali-metal, so I could be sodium. EDIT: Okay, we have bonds to chlorine, iodine, carbon, hydrogen (moves like a river -> water) and something I don't know. We need to sort them after these hints and maybe use there atomic numbers in the formula. (iodine: 53, hydrogen:1, carbon:6, chlorine: 17, and one number I am missing.)

Answer 5

Work in progress.

I think @Nefer007 has the right idea for the first 3 paragraphs.

Paragraph 4:

I'm always moving,
with no need to stop.
I've no place to be going,
but it doesn't matter - I'm first!

I think it has to do with

the sun, although I can't seem to find anything that seems relevant

For the very first paragraph,

it mentions nothing is more important than the bonds on my family so I started thinking about electrical bonds and having something to do with the nutrition label. So far there is no connection between the two that I see other than that.

For the equation,

I think the paragraph about the family determines the order. My first brother is always the same (Eulers constant or gravitational constant), the next is narcissitic(negative '-') Another brother moves like a river(no idea), His twin is impossible(i),My sister can be quite quiet, but when she's angry you don't want to hear her hiss(possibly square root since it looks like a snake and has a positive and negative answer maybe referring to her mood?)

I don't think I'll be able to finish this but there's some stuff to think about. I'll delete this post if someone finishes before me.

[I'd suggest this has something to do with Euler's Identity. e^ipi = cospi + isinpi Cosine moves like a river, iSine is impossible, the swiss cheese fan is Euler's number, the narcissist is pi because it goes on and on about itself (easy as pie idiom) -- don't know how the nutrisional facts fit in

I'm not sure if the "it's a sign you've been released" paragraph is referencing CO2 in reference to cosine being squared. Make what you will of that.

So the six terms are e^i, e^pi, isinpi, cospi, i, and pi. I think. But where does the 27 come from?]