# Hidden Number Sequence

Oh!

There is a number sequence hidden in here, but where?

Here are just a few examples so I will make the answer multiple choice. Can you find the sequence, the pattern, and the choice that follows the same pattern? I hope this isn't too broad and only one pattern matches.

OPTION 1

I'm the first and obviously best option. You should really pick me. Don't you want to be number one? You don't even need to read the other options. Just stop right here. Your gut is telling you I'm the right choice, isn't it? I know it is. If you keep reading, they're going to try to convince you that they're really the best answers and that's just going to confuse you. Have you ever felt silly because you didn't go with your gut? You let yourself be swayed by smooth talkers and regretted it, right? Don't let that happen to you here. Be strong. Be vigilant. I'm right and you know it. Go ahead, post an answer. Vote for Option 1. Of course, you have to figure out why.

OPTION 2

Look, I know I'm the middle answer so I don't get the first word or the final word. I'm going to have to convince you in another way. I will be the most helpful. I'm nice enough - and desperate enough - to give you a hint. I'm the middle answer and I'm also the answer of medium length. Maybe the length matters. Maybe the length doesn't matter. I'm not telling. I'm going to help you. Yes, I am. No, we're not; now, shut up! He doesn't know what he's talking about. We're not going to help no stinkin' puzzle solver to solve our puzzle. We hates the filthy puzzlers. We hates them! Look, I'm really sorry about that guy. He doesn't speak for all of us. I want to help and the hint I gave it totally a legitimate hint. Honest. It's not a red herring at all. Or is it? I don't know. Well, I do know but I'm not telling you. Can you count in different bases? How about two bases at once? How would you do that? Good luck.

OPTION 3

Save the best for last, right? I am so incredibly superior to the other jokers that it's not funny any more. Really, I just feel bad for them. They are truly inadequate and have no idea. Poor, poor other answers. You know how, when someone is dead, it's only sad for other people? It's the same way when you're a wrong answer. They don't know they're wrong, but they are. Of course, you might want some proof, so here it is. It's simple, really. I am by far the longest answer. I hold the most text and, therefore, hold the most ideas. Ideas are from creative minds. Creative minds are better than dull minds. Because creative minds are better, they produce ideas, and I have the most ideas, I am clearly better. QED. It's simple, really. I tried explaining this to them one time but they just stared at me with a dull expression on their face. I don't think they really followed me at all. I'm not even sure they were listening, to be honest. They get the far away look in their eyes whenever I try explaining things. Obviously, that is more evidence of their dullness. Pick the best, pick me: Option Three.

HINT 1

The hints from Option 2 are legitimate. You're going to need to need a base besides base 10. Which base? Well, which option is helpful?

• So, one needs to find a match between first part and one of the 3 other parts, correct? Commented Oct 27, 2015 at 7:31
• @klm123 Right. One of the options continues the number sequence started by the first part. Commented Oct 27, 2015 at 10:58

The hidden sequence is:

$2$ $10$ $42$ (here I knew it must be the right one) $170$ $682$

or in binary:

$10$ $1010$ $101010$ $10101010$ $1010101010$

How to find it?

Count the letters (ignoring whitespace and punctuation) of each paragraph. The first four numbers are from the intro. The three options have $512$, $682$ and $852$ letters. Therefore option 2 is the matching one.

• except the last paragraph has 40 words, not 42 Commented Oct 29, 2015 at 15:59
• @dperry Count letters, not words. Commented Oct 29, 2015 at 16:01
• ah, you're right, I misread Commented Oct 29, 2015 at 16:02

Here goes a very wild guess:

The sequence is 1, 1, 2, 6, 33; the representation of $n!$ in base 7, and it's coded for in the amount of punctuation marks per paragraph. The correct answer would then be option 1.

Rationale:

What caught my attention was the splitting of the intro text into four paragraphs, and for some reason the wording in the options made me focus on the punctuation.
Counting the punctuation marks (including ') yields 1, 1, 2, 6 for the intro and 33, 55 and 52 for options 1, 2 and 3 respectively.

I then searched for such sequences on oeis.org, and only "1, 1, 2, 6, 33" seems to be listed there. Searching for the other two options yields no results.
The most likely candidate for a sequence starting with 1, 1, 2, 6, 33 is, as I mentioned, the representations of $n!$ in base 7 — kind of an obscure one, but since option 2 hinted at "bases", it may not be completely impossible.

This is probably way off, but at least from here it seems remotely plausible.

• This reminds me of how "what do you get when you multiply six by nine" is 42 if you're working in base 13. Excellent find! I'll add something to help narrow. Commented Oct 28, 2015 at 19:15