# Time Series Analysis

The next semester you plan on following a course

about Time Series Analysis. Unfortunately, you have no idea when the courses
will be held. The past few days you have received some cryptic messages. Given below
is an overview of
the messages you
received along with their time and date.

Can you
figure out when the course
is going to start?

Day 1 (1 January):
05:02 p.m. - caob
11:05 p.m. - lipscarkb

Day 2:
05:11 a.m. - kcaharcak
06:17 p.m. - hca
08:23 p.m. - caob

Day 3:
01:31 a.m. (Delayed message from day 2) - behcab
09:41 p.m. - hsibe

Day 4:
09:47 a.m. - cafalb
03:59 p.m. - kblipsibe
05:07 p.m. - cap

Day 5:
02:13 a.m. - mghkca
08:23 p.m. - albkkhnb

Day 6:
05:37 a.m. - hararftibk
07:43 a.m. - kbtifararh
08:49 a.m. - bnhkkbal
10:07 a.m. - cakhmg

Note: "seconds" are important...

Hint:

While the "seconds" are important, they aren't necessary in solving this puzzle; they just provide a clue on how to decode the messages. If you want to find these "seconds", look outside the box (both literally and figuratively)...

• I have a feeling that the numbers are representation of the text above :) – Techidiot Jan 22 '17 at 11:56
• @Techidiot: both the numbers and the text are important, but they are unrelated ;) – Levieux Jan 24 '17 at 9:55
• I imagine reviewing the Wikipedia page on how to calculate TSA would be helpful based on the times given converted to decimal.. – mkinson Jan 25 '17 at 3:09
• @mkinson: I can assure you no knowledge of TSA is required to solve this. It just seemed like a fun title, because what you need to do is analyze a series of times ;) The times provided are actually based on two different, intertwined, series. – Levieux Jan 25 '17 at 9:28

I rearranged the dates to a one-per-row format which might be easier to process:
01/01 05:02 p.m. - caob
01/01 11:05 p.m. - lipscarkb
01/02 05:11 a.m. - kcaharcak
01/02 06:17 p.m. - hca
01/02 08:23 p.m. - caob
01/03 01:31 a.m. (Delayed message from day 2) - behcab
01/03 09:41 p.m. - hsibe
01/04 09:47 a.m. - cafalb
01/04 03:59 p.m. - kblipsibe
01/04 05:07 p.m. - cap
01/05 02:13 a.m. - mghkca
01/05 08:23 p.m. - albkkhnb
01/06 05:37 a.m. - hararftibk
01/06 07:43 a.m. - kbtifararh
01/06 08:49 a.m. - bnhkkbal
01/06 10:07 a.m. - cakhmg

Regarding the strings

'c' is always followed by an 'a', which might mean, that it is actually the character sequence 'ca' that means something. Furthermore, if we suppose 'mg' is also a two-character symbol, then the string 'ca-k-h-mg' is actually the reverse of 'mg-h-k-ca', which both appear as messages. In a similar fashion, 'h-ar-ar-f-ti-b-k' is the reverse of 'k-b-ti-f-ar-ar-h' and 'al-b-k-k-h-n-b' is the reverse of 'b-n-h-k-k-b-la', all of them being messages.

Actually it seems,

these strings have to be split into short forms of chemical elements, and their atomic numbers should be used. Then these atomic numbers should be turned into letters of the english alphabet (1=a, 2=b, and so on...) to get a sensible message.

For example message 2,

lipscarkb
split into chemical elements: Li P Sc Ar K B
atomic numbers: 3 15 22 18 19 5
to letters: course

Using this encoding, the messages give:

'the course starts at the date and time second to last message arrives sevirra egassem tsal', in which the last 3 words are probably just filler, mirrored words of the important part of the messages. I'm not a native english speaker, but if I get it right, we have to figure out the pattern in the date and time of future messages, especially when the 'second to last' will arrive, and that moment will be the start of the course.

There is something strange

with the alignment and break of the paragraphs in the question (that is, outside of the message box). But I haven't yet figured out what's going on with it.

I noticed, that minutes are actually

every second prime number modulo 60. (To analyze the hours, maybe we have to care about the carry.)

The hours

(after removing the carry) are an enumeration of the letters in the keyboard layout-order converted to numbers: Q, W, E, ... = 17, 23, 5, ... = 5pm, 11pm, 5am, ..., and this also explans, why there is a delayed message during the night between the second and third days: the alphabet has 26 letters, while there are only 24 hours in a day - letters X, Y and Z will cause a small delay.

The length of

the alphabet is 26, and the original message had 13 words, so together with the mirrored words it will consist of 26 messages too. This suggests that what we are interested in is the expected arrival of the 25th message (or the 24th, if my English is poor - I'm not sure I get the concept of 'second to last' right; is it the penultimate or the antepenultimate element of a sequence?). We already have an idea at what time this will be (the 2x25+1=51th prime is 227, the 25th letter on the keyboard N, which corresponds to 14 hours and 227 minutes, that is 5:47pm), but still have to figure out the day.

The day

is the earliest possible to get a chronological order. That gives us 9th January, if my numbers are correct.

Here I include a table to summarize these findings in an easy-to-digest format:

     ||      minutes     ||              hours               ||               ||
||                  ||                                  ||               ||
|    || (2N+1)th | prime || prime | Nth | to |   # + |   sum ||       |       ||   chemical | converted |
|  N ||    prime | mod60 || div60 | key |  # | carry | mod24 ||  time |  date ||    message |   message |
+----++----------+-------++-------+-----+----+-------+-------++-------+-------++------------+-----------+
|  1 ||        2 |     2 ||     0 |   Q | 17 |    17 |    17 || 17:02 | 01/01 ||       CaOB |       THE |
|  2 ||        5 |     5 ||     0 |   W | 23 |    23 |    23 || 23:05 | 01/01 ||  LiPScArKB |    COURSE |
|  3 ||       11 |    11 ||     0 |   E |  5 |     5 |     5 || 05:11 | 01/02 ||  KCaHArCaK |    STARTS |
|  4 ||       17 |    17 ||     0 |   R | 18 |    18 |    18 || 18:17 | 01/02 ||        HCa |        AT |
|  5 ||       23 |    23 ||     0 |   T | 20 |    20 |    20 || 20:23 | 01/02 ||       CaOB |       THE |
|  6 ||       31 |    31 ||     0 |   Y | 25 |    25 |     1 || 01:31 | 01/03 ||     BeHCaB |      DATE |
|  7 ||       41 |    41 ||     0 |   U | 21 |    21 |    21 || 21:41 | 01/03 ||      HSiBe |       AND |
|  8 ||       47 |    47 ||     0 |   I |  9 |     9 |     9 || 09:47 | 01/04 ||     CaFAlB |      TIME |
|  9 ||       59 |    59 ||     0 |   O | 15 |    15 |    15 || 15:59 | 01/04 ||  KBLiPSiBe |    SECOND |
| 10 ||       67 |     7 ||     1 |   P | 16 |    17 |    17 || 17:07 | 01/04 ||        CaP |        TO |
| 11 ||       73 |    13 ||     1 |   A |  1 |     2 |     2 || 02:13 | 01/05 ||     MgHKCa |      LAST |
| 12 ||       83 |    23 ||     1 |   S | 19 |    20 |    20 || 20:23 | 01/05 ||   AlBKKHNB |   MESSAGE |
| 13 ||       97 |    37 ||     1 |   D |  4 |     5 |     5 || 05:37 | 01/06 || HArArFTiBK |   ARRIVES |
| 14 ||      103 |    43 ||     1 |   F |  6 |     7 |     7 || 07:43 | 01/06 || KBTiFArArH |   SEVIRRA |
| 15 ||      109 |    49 ||     1 |   G |  7 |     8 |     8 || 08:49 | 01/06 ||   BNHKKBAl |   EGASSEM |
| 16 ||      127 |     7 ||     2 |   H |  8 |    10 |    10 || 10:07 | 01/06 ||     CaKHMg |      TSAL |
| 17 ||      137 |    17 ||     2 |   J | 10 |    12 |    12 || 12:17 | 01/06 ||        PCa |        OT |
| 18 ||      149 |    29 ||     2 |   K | 11 |    13 |    13 || 13:29 | 01/06 ||  BeSiPLiBK |    DNOCES |
| 19 ||      157 |    37 ||     2 |   L | 12 |    14 |    14 || 14:37 | 01/06 ||     BAlFCa |      EMIT |
| 20 ||      167 |    47 ||     2 |   Z | 26 |    28 |     4 || 04:47 | 01/07 ||      BeSiH |       DNA |
| 21 ||      179 |    59 ||     2 |   X | 24 |    26 |     2 || 02:59 | 01/08 ||     BCaHBe |      ETAD |
| 22 ||      191 |    11 ||     3 |   C |  3 |     6 |     6 || 06:11 | 01/08 ||       BOCa |       EHT |
| 23 ||      197 |    17 ||     3 |   V | 22 |    25 |     1 || 01:17 | 01/09 ||        CaH |        TA |
| 24 ||      211 |    31 ||     3 |   B |  2 |     5 |     5 || 05:31 | 01/09 ||  KCaArHCaK |    STRATS |
| 25 ||      227 |    47 ||     3 |   N | 14 |    17 |    17 || 17:47 | 01/09 ||  BKArScPLi |    ESRUOC |
| 26 ||      233 |    53 ||     3 |   M | 13 |    16 |    16 || 16:53 | 01/10 ||       BOCa |       EHT |

• Nice start! And carry is indeed important. – Levieux Jan 25 '17 at 10:23
• You've got it exactly right! Nice overview as well :) – Levieux Jan 25 '17 at 22:42