7
$\begingroup$

What is the missing number in this cyclic sequence? It would require a notation convention not seen here to fit into the scheme here.

$$\phantom{ \textrm{(repeat)} } \quad\textbf{?}~~ \,,~~ 2.4 \,,~~ 1 \,,~~ 36.0 \,,~~ 1 \,,~~ 8 \,,~~ 1 \,,~~ 15 \,,~~ 2.4 \,,~~ 1 \,,~~ 8.0 \,,~~ \frac{~9~}2 , \phantom{ \,,~ \dots } \\ \textrm{(repeat)} \quad\textbf{?}~~ \,,~~ 2.4 \,,~~ 1 \,,~~ 36.0 \,,~ \dots \phantom{ \,,~~ 1 \,,~~ 8 \,,~~ 1 \,,~~ 15 \,,~~ 2.4 \,,~~ 1 \,,~~ 8.0 \,,~~ \frac{~9~}2 , } $$

Hintified from comments:

$8$ vs $8.0\,$?   $2.4$ vs $\frac92$?   All relevant properties, including the visual one, are mathematical.

Half$/$ hint:

The visible clue: $2.4$, $36.0$, $2.4$ and $8.0$ are not represented as reduced fractions.

$\endgroup$
  • $\begingroup$ Is it significant that one number is $8$ while another is $8.0$? $\endgroup$ – GentlePurpleRain Feb 3 '16 at 22:23
  • $\begingroup$ I think 'visual' is a hint, but I can't figure out how it helps. I've been looking at ways to measure visual acuity, but can't see how any of the numbers fit. $\endgroup$ – jhabbott Feb 4 '16 at 1:42
  • $\begingroup$ Is the sequence cyclic? $\endgroup$ – 2012rcampion Feb 4 '16 at 6:00
  • $\begingroup$ The above comments have prompted a more-periodic layout and a "Hintified from comments" fortune cookie $\endgroup$ – humn Feb 4 '16 at 7:29
  • $\begingroup$ Your hints are very... hinty. Any more? $\endgroup$ – question_asker Feb 15 '16 at 20:38
3
$\begingroup$

Your old friend question_asker here. I've got the answer, and it's

$3.\overline{3}$ or $3.333...$

Why, you ask?

Who knows!

Well, then how did I get the answer?

Brute force! Kind of!

(record scratch) lol what

Yeah, look, I went to college for like 1.5 semesters before dropping out, and during the semester I liked, I took Calculus I, and while I enjoyed it, it was the last of my formal math education.

Anyway, the kind (non-, as per their profile) doctor had at one point left a hint on this question: "This sequence rolled out in reverse order as reciprocals for a probability problem here." In a brief chat with Pangloss, they mentioned that the sequence was only of importance with regard to games where randomness was necessary (emphasis mine). From this I could narrow down that the problem I was looking for probably involved dice or a coin flip. Skimming those problems, I found that, lo and behold, there was a problem that involved both, and specifically an answer that had the exact thing mentioned in the hint. I "checked" the "math" briefly and realized that it was, in fact, the reciprocals of the elements of the sequence in reverse. From this I could conclude that the missing value was $10/3$, and since it was mentioned that the missing element required a notation convention not already seen in the puzzle, I realized it must be $3.\overline{3}$ or $3.333...$

As such, with Pangloss's blessing, I am posting this answer and awaiting my parade.

| improve this answer | |
$\endgroup$
  • $\begingroup$ Cheers to a solution that marshals so many resources! The purely mathematical approach had its chance for half a month before you revived this puzzle. $\endgroup$ – humn Feb 18 '16 at 21:36
  • $\begingroup$ @Pangloss I may not be educated, but I'm resourceful, dammit $\endgroup$ – question_asker Feb 18 '16 at 21:37
  • $\begingroup$ The old chat room is open again if you'd like to add to this solution $\endgroup$ – humn Jul 3 '16 at 12:03
1
$\begingroup$

Possibly halfway to a solution, here's my worksheet so far.

\begin{matrix} & 9&~~?~~& 12 & 1 & 36 & 1 & 8 & 1 & 15 & 12 & 1 & 8 & 9 &~~?~~& 12 & \\[-1ex] \cdots & -& &\cdot& - &\cdot& - & - & - &-\!\!-&\cdot& - &\cdot& - & &\cdot& \cdots \\[-1ex] & 2& ? & 5 & 1 & 1 & 1 & 1 & 1 & 1 & 5 & 1 & 1 & 2 & ? & 5 & \end{matrix} Think I could almost stagger the rest of the way,

without fully figuring out the rule. Then again, what was that about notation convention?

| improve this answer | |
$\endgroup$
  • 1
    $\begingroup$ Pangloss, I hate you. $\endgroup$ – question_asker Feb 16 '16 at 12:27
  • 1
    $\begingroup$ For the record, that's my upvote you're seeing on this answer, as well as that on your comment. $\endgroup$ – question_asker Feb 16 '16 at 12:33
  • 1
    $\begingroup$ When you refer to a "notation convention", are you referring to this thing above with the dots and dashes, or something entirely separate? $\endgroup$ – question_asker Feb 17 '16 at 13:19
  • 1
    $\begingroup$ I thought that might be the case, I just wanted to get every possibility I had considered onto the page, so to speak, in case it jumpstarted anybody else's thought processes. $\endgroup$ – question_asker Feb 17 '16 at 19:16

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.