Meatsacks, please help us decipher this code

Question

Be greeted, meatsacks. We have been studying several of your species for some time now. One of the subjects, some meatsack related to saving Earth several times, seemed to know a lot of our operations and we believe we have found information that is critical to the success of our latest operation... in their brain. The subject did not give up this information willingly, so we had to... pull... this information directly from the subject's brain. Unfortunately, the subject expired after these... mundane... experiments. Attempts to uncover the true nature of our data by plugging the data directly into another subject's brain only produced a pungent smell seemingly unrelated to the information itself.

Since this information came from a meatsack, maybe another living meatsack can decode this information for us. In return we can offer recycled imprints of furballs, or additional real imaginary numbers.

The information we pulled from the... subject... appeared to have 7 states. Once the correct translation for each of the states have been found, we believe this data to be decoded as a sentence. We do not fully understand why the data we recovered only had 7 states, as simple meatspeak has about 26 unique representations.

We will provide you the data in both a digital QR-format (for moveable devices for furball imprints) and numerical format (for devices where copying such data is not a problem).

260504040140406302560010302560010303020560501604013025600404001030256001056001302560401300302560501404010302605040401404063020560604040130256050401401030302605040401404063025604013002560504014010303025605014040103025605040140103025600103025600404001030260404063020560060606013030256050140103025600404001030302560010560013020560604040130

We may be able to share some of our initial research on this matter if you deem it necessary.

Our findings on meatsack subjects (Hint 1)

We believe these notes with our research on the bipedal race "meatsacks" could proof useful in uncovering the message in the code we retrieved from our expired test subject.

Meatsacks are a race of bipedal creatures. When observed in their natural habitat, these creatures tend to flock to two distinct places, traveling vast distances between those two places with basic machinery. Most meatsack individuals are obsessed with a rectangular object in one of those places, where they spend up to a third of their time in a horizontal position. Meatsack individuals communicate by means of air movement, which seems inefficient. Some individuals are part of a hivemind that calls itself "world wide web". Lacking other options, this seems to be the most efficient way of communicating with these beings if necessary.

Analysis on the abducted individuals of this race show an inefficient large structure around an otherwise small computational core. The fact that this computational core seems only capable of having one of seven distinct states at a time shows how inferior this species is compared to us. Data about these distinct states will be encoded with a through g0 through 6. These computational states refer t[REDACTED].

External stimulation of the computational core of meatsack individuals results causes the computational core to cease functioning. The meatsack hivement seems to respond better. The hivement seems obsessed with static imprints of furballs and meaningless numbers. We might be able to use this fact to our advantage.

Addendum: Meatsacks seem to refer to the computational core as a "brain".

Meatsack communication (Hint 2)

We have translated our research on meatspeak and communication of meatsack subjects for you.

Meatspeak subjects communicate via the following means:

• Movement of air. Meatsacks have recepticles near their computational core to decode the patterns. Information density is low. Decoding the signal is simple, but producing a signal is significantly harder. Due to the limited reach and low information density, this method of communication is not worth our time.
• The hivemind. Meatsacks communicate via a number sequence. Information density is low, but throughput is high. An easily identifiable sequence of numbers is used to encode imprints. We are unsure how to decode these imprints, but most imprints are stored with meatspeak sentences that allows us to identify what they should encode. The hivemind seems capable of producing information at will and seems only limited by the throughput of information channels. We can easily change this by accessing the hivemind from multiple access points. It's unclear how meatsacks interface with the hivemind. Our research has not succeeded plugging their computational core into their hivemind.

The state sequence recovered from the computational core of the deceased subject does not seem to be any of these things. There are too many states to decode the sequence as air movement, even if part of the sequence is to signify timing. There are far too little states to decode as simple meatspeak used in the hivemind. Complex meatspeak seems to use even more states. The sequence is not of one of over 50 imprint formats we found.

Do meatsacks communicate in an other way? We have not found a significant amount of signals between the computational cores of any meatsacks we have studied. Meatsacks leave pheromone trails, but they seem ineffective in communicating anything. Meatsacks move around "food" items, but besides those they move around lots of other mundane items. Some of these are "tools" and things to protect them from the environment. A lot of these objects seem completely useless. The objects seem of similar size, and show similar signal readings. There is no significant alpha or beta decay, no significant heat signal, no significant energy reading. Could they be communicating something with the number of these items? That seems even more inefficient than communicating with air movement.

Another message (Hint 3)

We extracted this message from a different meatsack. Maybe giving you more data to work with helps?

2560013002604040630256050140103025605040140103025604013002560504014010302056060404013025605014010302560013002604040630205600606060130256001030205605016040130302560504014010302604040630256004040010302560010560013020560060606013026050140560140630302560501401030260501405601406302560504014010302056060404013025605040140103030260504040140406302560010302560013002560504014010302604040630205606040401303025600401030260504040140406302604040630256050140103030205606040401302560504014010302560504014010303026050404014040630260404063020560501604013025605014010302605014056014063025600130026040406302056006060601303025605014010302605014056014063025605040140103020560501604013030256050401401300256050401401030256050401401030256001030302605040401404063026040406302560405601401030302560501401030260501405601406302560504014010302056050160401303020560604040130256050401401030260404063020560604040130256050401401030302605014056014063025605040140103026050404014040630256050140103030256050401401030256001030256050401401030256004010302560501401030256040130025600130025600401030256001300256050140103020560501604013030260504040140406302604040630256040560140103030260504040140406302560010302560040404013002605014056014063026050404014040630302560040400103025604013003025605014040103025605040140103025605014010302605040401404063030256040560140103025605040140103025600401030260504040140406302056050160401303025605014040103025600105600130256050140103030256050140103026050140560140630256050401401030205605016040130302560010302605040401404063025600401030260501405601406303025605040140103020560501604013025605040140103020560604040130302560501401030256004040010303020560604040130256050401401030256050401401030302560501401030260501405601406302560504014010303053602012053602013025600404001030256040130025600103025604056014010303026050404014040630205606040401303053602012053602013025605040140103030256040560140103025600404001030

_{Author's note: I believe this puzzle to be solvable both with and without computer knowledge. I would recommend starting with the cipher part.}

Answer 1

So, from Sleafar's cracking of the cipher, we now know the cryptic hints were referring to the fact that

aliens have to resort to analyzing energy and heat levels because they can't see.

So, it figures that if the cipher referred to meatspeak in the way we usually process it, and not in a way suited to the aliens' usual way to process raw data, it would be hard for them to get.

as in, the data describes the way we would draw the letters, which the aliens have no way of knowing.

For some extra evidence of this other than the hint, we can look at the fact that an O: 256001056001 looks a lot like two Ls: 2560010, probably because an O can be made with one L and one inverted L.

Deducing what each state actually means is now not that hard:

All letters start with 2 and end with 3, so the meaning of those is probably some sort of start/end delimiter.

0 appears a lot, so it's probably the drawing command.

4 and 6 are clear when you look at S: 205606040401, and realize that an S can be made with two left turns and two right turns (no matter if you're starting from the top or bottom), so 6 must be the left turn and 4 must be the right turn.

This leaves 5 and 1. I had noticed from Gareth's post that there are as many 1s as there are 5s, and furthermore, they are perfectly nested, so they must be somehow related. Turns out 5 saves the current location of the hand, and 1 restores it.

From this, we can gather that the states refer to the following:

0 = forward
1 = load position
2 = pen down
3 = pen up
4 = turn right
5 = save position
6 = turn left

Following these commands, we would get the following message:

"ALL YOUR BASE ARE BELONG TO US"

For fun, this is how the message in the hint looks like after it's decoded:

"INTERESTINGLY ENOUGH, THESE ALIENS CANT SEE ANYTHING THEY FEEL AND THEY SENSE HEAT ELECTRICITY AND ALPHA OR BETA DECAY BUT THEY LACK EYES TO SEE THE WORLD AS WE DO"

Answer 2

Analysis:

Using the new message from the 3rd hint I took a closer look at the patterns at the beginning and end of each message:



The interesting parts here are the places where 2 of this patterns meet. They seem to be separated by a 30. Therefore I assumed 30 would be used as a separator for letters and 3030 as a separator for words. Replacing the codes between the separators with single letters and feeding them to http://quipqiup.com resulted in some nonsense, but it returned also a couple of words which I used as a starting point. Splitting by 30 seems to work partially, there seem to be superfluous 0 in the code. I could finally split and decode both messages correctly.

Code 1:

260504040140406 30 2560010 30 2560010 3030
2056050160401 30 256004040010 30 256001056001 30 2560401 30030
2560501404010 30 260504040140406 30 205606040401 30 2560504014010 3030
260504040140406 30 2560401 300 2560504014010 3030
2560501404010 30 2560504014010 30 2560010 30 256004040010 30 26040406 30 2056006060601 3030
25605014010 30 256004040010 3030
256001056001 30 205606040401 30

This decodes to:

ALL YOUR BASE ARE BELONG TO US

Code 2:

256001 300 26040406 30 25605014010 30 2560504014010 30 2560401 300 2560504014010 30 205606040401 302560501401030 256001 300 26040406 30 2056006060601 30 2560010 30 2056050160401 3030
2560504014010 30 26040406 30 256004040010 30 256001056001 30 2056006060601 30 260501405601406 3030
25605014010 30 260501405601406 30 2560504014010 30 205606040401 30 2560504014010 3030
260504040140406 30 2560010 30 256001 300 2560504014010 30 26040406 30 205606040401 3030
256004010 30 260504040140406 30 26040406 30 25605014010 3030
205606040401 30 2560504014010 30 2560504014010 3030
260504040140406 30 26040406 30 2056050160401 30 25605014010 30 260501405601406 30 256001 300 26040406 30 2056006060601 3030
25605014010 30 260501405601406 30 2560504014010 30 2056050160401 3030
256050401401 300 2560504014010 30 2560504014010 30 2560010 3030
260504040140406 30 26040406 30 25604056014010 3030
25605014010 30 260501405601406 30 2560504014010 30 2056050160401 3030
205606040401 30 2560504014010 30 26040406 30 205606040401 30 2560504014010 3030
260501405601406 30 2560504014010 30 260504040140406 30 25605014010 3030
2560504014010 30 2560010 30 2560504014010 30 256004010 30 25605014010 30 2560401 300 256001 300 256004010 30 256001 300 25605014010 30 2056050160401 3030
260504040140406 30 26040406 30 25604056014010 3030
260504040140406 30 2560010 30 256004040401 300 260501405601406 30 260504040140406 3030
256004040010 30 2560401 30030
2560501404010 30 2560504014010 30 25605014010 30 260504040140406 3030
25604056014010 30 2560504014010 30 256004010 30 260504040140406 30 2056050160401 3030
2560501404010 30 256001056001 30 25605014010 3030
25605014010 30 260501405601406 30 2560504014010 30 2056050160401 3030
2560010 30 260504040140406 30 256004010 30 260501405601406 3030
2560504014010 30 2056050160401 30 2560504014010 30 205606040401 3030
25605014010 30 256004040010 3030
205606040401 30 2560504014010 30 2560504014010 3030
25605014010 30 260501405601406 30 2560504014010 3030
5360201205360201 30 256004040010 30 2560401 300 2560010 30 25604056014010 3030
260504040140406 30 205606040401 3030
5360201205360201 30 2560504014010 3030
25604056014010 30 256004040010 30

This decodes to:

INTERESTINGLY ENOUGH THESE ALIENS CANT SEE ANYTHING THEY FEEL AND THEY SENSE HEAT ELECTRICITY AND ALPHA OR BETA DECAY BUT THEY LACH [sic] EYES TO SEE THE WORLD AS WE DO

Observations:

I still don't know what the states exactly represent. It could be related to hand movements while the letters are written or to eye movements when they are read. This is supported by the similarity of codes for some letters. For instance F is encoded as 256050401401 and E is encoded as 2560504014010. Another example is I encoded as 256001 and L encoded as 2560010. There is also a problem with the letter K which is encoded the same as H.

Interesting fact:

Translating the meatsack states to notes produces a melody:

Variant 1
Variant 2

Answer 3

Some remarks that may be useful to someone (this is nothing resembling an answer at present, and I don't think any of it needs spoilering):

The ciphertext has length 336 = 16*3*7. The counts of 0,1,2,3,4,5,6 are respectively 144,32,24,30,38,32,36. So the number of 0s is notably bigger than the others, but the differences between those others seem like noise rather than signal.

The number of 0s happens to be exactly 3/7 the number of symbols. There aren't exactly three 0s in every block of 7 consecutive symbols. I haven't looked to see whether some other way of dividing the ciphertext into sevens produces exactly one 0 in each.

The prevalence of zeros might suggest that some sort of run-length encoding is going on here (e.g., zeros are counts of successive 1-bits separated by single 0s or vice versa) but (1) in that case we should expect zeros to be about half the ciphertext and (2) we should also expect there to be a continued falloff from 0 to 1 to 2 etc. I tried interpreting it this way anyway but the result didn't look very plausible.

If the 0s were distributed at random we would expect to see (3/7)^2*335~=62 instances of "00" but in fact there are only 16. Perhaps that's chance but my guess is that it's real, that there's some reason why 0s are less likely to be followed by 0s than non-0s are. The counts of x0 are 16, 14, 4, 30, 38, 10, 32 for x=0,1,2,3,4,5,6, which looks like there may be nonrandom nonuniformity going on.

Here, in fact, are the frequencies of all 49 pairs: 16 32 23 18 29 16 9 14 0 0 8 9 0 1 4 0 0 0 0 16 4 30 0 0 0 0 0 0 38 0 0 0 0 0 0 10 0 0 0 0 0 22 32 0 0 4 0 0 0

Row number is first item in pair, column number is second. This counts all pairs (01 12 23 34 etc., rather than 01 23 45 etc.) which may or may not be a mistake. If we do it the other way (01 23 45 ...) we get these counts: 8 15 7 9 18 6 5 7 0 0 3 6 0 1 3 0 0 0 0 12 2 17 0 0 0 0 0 0 14 0 0 0 0 0 0 7 0 0 0 0 0 7 20 0 0 1 0 0 0

This looks enough like half the previous table that I suspect we shouldn't be breaking the ciphertext into pairs and using them, even though some pairs may be significant sometimes.

What are there seven of? Pitch-classes in a diatonic scale. Colours of the rainbow (mostly because Newton thought 7 was a magic number). Deadly sins. Days of the week. Planets other than earth (sorry, Pluto). Wonders of the World. Lots of other things where people have made lists and tuned them to have seven elements. Bits in an ASCII character. Colours needed to colour an arbitrary map drawn on a torus :-). None of that seems very helpful.

That's probably enough meaningless numbers for now. I regret that I have no furballs to offer.

---

Some further thoughts consequent on hint 2:

First of all, looking at patterns of repetition in the message gives further reason to think that the numbers aren't consistently in pairs, nor indeed groups of any fixed size. (I haven't checked, though, whether this looks different if we e.g. treat 00 separately or ignore zeros.)

As a little more evidence that larger-scale patterns are present, here is an array like the ones above for frequencies of digits 2 apart: 80 10 1 13 12 16 11 18 0 0 12 0 2 0 4 0 0 0 0 4 16 2 0 22 5 0 0 0 3 17 0 0 14 0 4 22 4 0 0 6 0 0 15 1 0 0 6 10 4

Quite different from the 1-apart ones, but there certainly seems to be some structure there. That isn't much evidence against (e.g.) digits being invariably in pairs, because of course successive letters in meatspeak aren't independent of one another.

Second, the hint suggests strongly that we should be looking for some other variety of meatsack communication that uses multiple similar-looking items. (Perhaps the 0..6 here are counts of those items.)

• Each Braille character is made up of up to six raised dots, but the number of 0s seems to rule that out, as do the frequencies of the different digits, as does the curious avoidance of adjacent matching digits.
• There were various "lamp-hanging" codes that had a similar sort of feel but I don't see how to get there from here, and in any case the hint indicates that whatever multiple thing we're looking for it doesn't radiate appreciable energy.
• I wondered about semaphore (though then the digits would need to be flag positions or something rather than object counts) but couldn't see a way to make that work.
• Prisoners' "knock codes" typically use pairs of numbers 1..5. This is kinda close, but (1) as mentioned above I don't think we're really working with pairs exactly, (2) 0..6 is quite different from 1..5, and (3) the distribution of pair frequencies seems like it has rather the wrong shape for anything much like this.
• A seven-segment display as on e.g. an old calculator could have its state described by a set of numbers 0..6. But however I slice it I think the frequency of 0s would require the things being displayed to be unrealistically "sparse".

I have the feeling I'm overlooking something obvious here.

Answer 4

Partial attempt

So the text has 7 different digits in the range of 0 and 6.
Some patterns suggest to me, that the digits should be read in pairs.
I noticed that only 20 of the 7x7=49 possible combinations appear in the text. The ones which have at least one 0 and 13,14,16,25,26,56,63. This might be a subset of the 26 'unique representations of meatspeak', i.e. letters of the english alphabet. However, it seems to be more complex than a simple substitution cipher, at least I didn't manage to find a solution in that direction yet.

Answer 5

This is a partial attempt, but I think I may be on the right track.

There are an awful lot of 0s, so it seems reasonable to me to use them as a delimiter. Replacing them with commas yields this sequence: 26,5,4,4,14,4,63,256,,1,3,256,,1,3,3,2,56,5,16,4,13,256,,4,4,,1,3,256,,1,56,,13,256,4,13,,3,256,5,14,4,1,3,26,5,4,4,14,4,63,2,56,6,4,4,13,256,5,4,14,1,3,3,26,5,4,4,14,4,63,256,4,13,,256,5,4,14,1,3,3,256,5,14,4,1,3,256,5,4,14,1,3,256,,1,3,256,,4,4,,1,3,26,4,4,63,2,56,,6,6,6,13,3,256,5,14,1,3,256,,4,4,,1,3,3,256,,1,56,,13,2,56,6,4,4,13,

On a hunch,

I've put in spaces wherever there were two zeros in a row: 26,5,4,4,14,4,63,256, ,1,3,256, ,1,3,3,2,56,5,16,4,13,256, ,4,4, ,1,3,256, ,1,56, ,13,256,4,13, ,3,256,5,14,4,1,3,26,5,4,4,14,4,63,2,56,6,4,4,13,256,5,4,14,1,3,3,26,5,4,4,14,4,63,256,4,13, ,256,5,4,14,1,3,3,256,5,14,4,1,3,256,5,4,14,1,3,256, ,1,3,256, ,4,4, ,1,3,26,4,4,63,2,56, ,6,6,6,13,3,256,5,14,1,3,256, ,4,4, ,1,3,3,256, ,1,56, ,13,2,56,6,4,4,13

Excluding spaces, this gives us the following

13 unique numbers: 1, 2, 3, 4, 5, 6, 13, 14, 16, 26, 56, 63, 256

There's only the digits 0-6 in the sequence, which could be

base 7. That means the decimal numbers are: 1, 2, 3, 4, 5, 6, 10, 11, 13, 20, 41, 45, 139

However, that sequence doesn't mean anything to me. Then again,

I removed all the 0s, using them for delimiters, which means the only valid digits remaining are 1-6. Maybe it's base 6, where 1 maps to 0, 2 to 1, etc? 0, 1, 2, 3, 4, 5, 2*, 3*, 6*, 11, 29, 32, 65

That doesn't make much sense, though, since the starred numbers would have a leading 0, which would be unnessesary.

Perhaps a cryptogram?

13 different numbers doesn't seem too strange for that, so I made the following substitutions: 1=A, 2=B, 3=C, 4=D, 5=E, 6=F, 13=G, 14=H, 16=I, 26=J, 56=K, 63=L, 256=M.

That gives us this potential cryptogram:

JEDDHDLM ACM ACCBKEIDGM DD ACM AK GMDG CMEHDACJEDDHDLBKFDDGMEDHACCJEDDHDLMDG MEDHACCMEHDACMEDHACM ACM DD ACJDDLBK FFFGCMEHACM DD ACCM AK GBKFDDG. However, there are some awfully long words in there, as well as a repeated word "DD", and a word starting "FFF", which I don't believe can be translated.

I think it's probable that there's additional steps needed, having to do with the actual values of the numbers, before doing any subsitutions, but at the moment I'm at a loss for what they may be.

Answer 6

Wrap-up of this puzzle

This is not a solution to the puzzle but provides notes from its poser. This type of answer has been approved by the community.

Caution: This post may contain spoilers.

---

Inspiration

I lurk every now and again on Puzzle.SE, and found the computer-puzzle questions interesting. However, a guess-the-digital-format question gets boring fast. I decided that I wanted to encode a sentence... in an unconvential way.

In my mind, there are two over-used onces:

• Various ciphers on natural text, usually yielding a similarly sized string.
• A base-x encoding, where we obfuscate the text by using the ascii numbers, and interpret it in a different format.

I thought of how we write things, and how text can have shapes. That's where I started my puzzle.

Creative steps

The first step was to decide on how to encode these shapes. I thought about L-Systems and Turtle graphics in particular. You can encode any shape in them, as long as you define the steps well. However, this would be a puzzle, which means that I had to obfuscate the steps involved in this. If I would have used a string such as b[LF[F]RF]Fa, the puzzle would have been solved within an hour.

After some looking around for easy shapes, I remembered that we could create letters with 7 segmented displays. After some searching around, I settled for this sheet:

Next up I created a simple Python program that took an arbitrary string and converted it to turtle graphics. After I was satisfied with that, I had to decide on the actual sentence people had to decode.

The sentence had to be something iconic - something people knew was correct when they found it - and something that ideally made some types of analysis harder.

Logistical steps

Now that I had a phrase, I decided to encode the characters I used to make turtle graphics to numbers. I had insider knowledge that the last two characters would always be the pen-up and forward event. In fact, this was a common delimiter between characters.

I deduced that from the numbers alone, it would be nearly impossible to find the turtle graphics. Especially because people did not know what they were looking for. However, due to the nature I generated my characters, there was a variable:1 substitution cipher that could be used. I briefly considered manually replacing some of the silly sequences, such as "penup forward penup forward" with a more efficient sequence, but this would break the substitution cipher that existed, and more importantly, would mess up any analysis people could do on the anonymous states.

In the end, the intended way of solving the problem was by simply analysing the string, finding the 2-character delimiter (30), then finding a suitable substitution after struggling a bit with characters that natively contained this sequence. Afterwards, knowing what the sequences encoded, I found it much more likely people would find the turtle graphics, as the steps were very basic for turtle graphics, and similar characters produced similar sequences.

Finishing touches

In the end, I still needed to present my puzzle. I wanted my audience to be able to find the strictly necessary information easily, but I did not want to present it on it's own. I could add some meaningless flavour text, but I decided to present it in the context of an alien species instead that would actually not be able to decipher the code. For additional humour I decided to present the aliens as beings that did see themselves as superiour beings, being able to do everything better than "meatsacks". In the end it turns out they are not capable of reading, and kind of "as blind as a bat". Furthermore, they identify someone that apparently played a fairly horrible video game as "some kind of hero", unable to distinguish between the virtual reality of video games and the actual reality. I also added some remarks about kittens and reputation.

Evolution

In the end, the puzzle seemed to be too difficult. People did some analysis, but did not get the breakthrough I hoped for. People seemed to return to trying to interpret this as base-7. The first hint was a subtile one where I gave some backstory, while also hinting that 0 thru 6 was not anything mathematics related.

Some useful information was posted after that hint, and I decided to wait it out a bit. People still were messing around with base-7, so I posted a more obvious hint about what 0 through 6 meant. It also contained some hints that would make the logical leap between sequences and the turtle graphics more managable.

Looking at the answers I got, the only thing people seemed to lack was data. I decided to encode another string, transcribing part of the second hint in it, and posting the sequence. This resulted in a rapid breakthrough.

Takeaway

I think this puzzle was slightly on the difficult side. Things I have learned:

• Don't encode distinct states without an order, without any relation to math, with numbers. People will try to use base-x for it, and waste a lot of time. I would probably try random characters.
• People liked the role-playing as an alien overlord in the comments. It might be worth repeating such a thing if appropriate.
• I am unsure if hiding hints in "research notes" (basically flavour text) is a good idea. In the end it was my intention to subtily push people in the right direction, but it might have been to subtile.
• People on Puzzle.SE can make crazy logical leaps. I should probably start my puzzles with just a little more information.

Answer 7

Partial answer.

If we replace all 00 for a space we got:
26050404014040630256
1030256
103030205605016040130256
404
1030256
1056
13025604013
302560501404010302605040401404063020560604040130256050401401030302605040401404
063025604013
25605040140103030256050140401030256050401401030256
1030256
404
103026040406302056
606060130302560501401030256
404
103030256
1056
13020560604040130

In which it seems like:

404 could be I since it appear several times..
Still don't know what else to do with the rest of the numbers but it seems important that they never get to 7, base 7 maybe.

Answer 8

Partial Attempt.

I converted the string to base-26 and got a 64 letters long sequence. Since it is 64, I tried box rotation algorithm but still not able to figure it out.

If anyone can take this up from here it would be great help.