# Just another day in the Shack

UPDATE - Per Stiv's answer below, there was in fact a mistake in the fourth row, eighth column of the diagram. Fixed diagram has replaced the errant one.

I work at the logistics base for a major remote research station in...well, I'm not supposed to say. Let's call Artanctica. It's a great job most days, because most messages are scheduled and routine. But today Hopkins is out, and that jerk Sandusky locked up the disk with the decoding program and is on his hourly 55 minute long smoke break. (I know, I know...it's written in COBOL and nobody knows how to maintain it or replace it.) So of course an urgent message arrives...

Captain Arbuthnot said he's going to transfer me to Ice Station Frasier-Heine if another urgent message doesn't get addressed pronto, so I'm hoping you can help. I do know the decoding program does not require any input other than the transmitted file, so I think everything you need is in there.

Hint 1:

The diagram above represents the full communication, not just the message. The communication includes overhead such as control and synchronization information. Unfortunately, that jerk Sandusky locked up the spec manual too.

Hint 2:

The synchronization data in the message is in four of the nine columns at right, and is related to the character in black on gray at left.

Hint 3:

In any given 3x3 grid, horizontal bold lines represent one number and vertical bold lines represent another. This representation is defined by a rule, not by arbitrary assignment.

Hint 4:

From the comments, the numbers in each 3x3 grid are coded in balanced ternary. Note also that the colors chosen for the middle squares are not arbitrary.

Hint 5:

If you need more Help!, ask the Beatles.

Hint 6:

Once you have letters, all of the key information you need is in the upper left rainbow-colored box. But there is still some figuring out to do.

Hint 7:

Substitution is performed on columns of the message with different keys which are generated from information given in the diagram.

Hint 8:

After substitution, there is one more action to be performed on the columns which is also keyed in the rainbow box at left.

The puzzle is entirely contained within the image; the text beforehand is purely for flavor - don't waste your time attempting to analyze its wording!

For any colorblind solvers, the vast majority of the puzzle is black, gray or white. The center of each 3x3 box is colored with a red/yellow checkerboard pattern, all of which have upper left corner red. The remaining coloration is in the 3x3 box in the upper left corner. In this box, the upper left, upper right, and lower right corners are white and violet, the upper center is black and green, the middle left is black and orange, the middle right is black and red, the lower left is black and yellow, and the lower center is black and blue.

This puzzle was inspired by Stiv's recent Captain Clumsy masterpiece, and is but a humble homage. I hope you enjoy!

Edit: please find below a text representation of the squares. The vertical lines, top to bottom, 1=black, 2=gray:

0000 0100 0010 0100 0010 0010 0100 0100 0010
0000 0010 0100 0010 0100 1000 0010 0100 1000
0000 0100 0100 0100 0100 0100 1000 0010 0100

0000 0100 0000 0010 0010 0010 0010 0010 0000
0000 0100 0000 1000 1000 0100 1000 0100 0000
0000 0010 0000 0010 0100 0100 0100 0100 0000

0000 0010 0010 0100 0010 0010 0100 0010 0010
0000 0100 0100 0010 0100 1000 0010 1000 1000
0000 0100 0100 0010 0100 0100 0100 0100 0100

0000 0100 0000 0100 0010 0100 0100 1000 0000
0000 0010 0000 0100 1000 0010 0010 1000 0000
0000 0100 0000 0010 0100 1000 0010 0010 0000

0000 0100 0010 0100 0010 0010 0010 0100 0010
0000 0010 0100 0100 0100 1000 1000 0010 1000
0000 0100 0100 0010 0100 0010 0100 0010 0100

0000 0010 0000 0010 0010 0100 0010 0010 0000
0000 1000 0000 1000 1000 0010 1000 1000 0000
0000 0010 0000 0100 0100 0010 0100 0010 0000


And the horizontal lines, top to bottom:

000 000 000 000 000 000 000 000
000 100 000 101 100 100 100 011
000 010 000 000 001 011 001 100
000 001 000 010 010 000 010 000

000 000 000 000 000 000 000 000
000 010 100 100 100 100 100 100
000 101 011 011 011 001 011 001
000 000 000 000 000 010 000 010

000 000 000 000 000 000 000 000
000 100 000 100 100 101 100 010
000 010 000 011 001 000 001 101
000 001 000 000 010 010 010 000

000 000 000 000 000 000 000 000
000 010 100 010 100 011 100 100
000 101 011 101 011 100 001 010
000 000 000 000 000 000 010 001

000 000 000 000 000 000 000 000
000 100 000 100 100 100 100 101
000 010 000 001 001 010 010 000
000 001 000 010 010 001 001 010

000 000 000 000 000 000 000 000
000 010 100 010 100 001 010 011
000 101 011 101 011 110 100 100
000 000 000 000 000 000 001 000

• Let me see what I can come up with. The way I developed the diagram unfortunately did not easily lend itself to a text transcription. Please give me a few... May 16 '20 at 21:15
• Haha! I thought I recognised the feel of the puzzle and it's wording - then I read the last paragraph :) I will look forward to seeing it solved or having a crack at it myself if my family can spare me some time! Looks like an interesting puzzle - nice work :)
– Stiv
May 16 '20 at 21:15
• I've attempted using ternary on the lines (did that day 1), but had no luck. Still not sure what the left diagrams could mean.
– Deusovi
May 20 '20 at 15:36
• @Deusovi: you are on the right track, but your attempt seems, if I may say, a bit rot13(haonynaprq). May 20 '20 at 15:40
• Ahh, I see. Unfortunately I don't have time to work on this until later tonight - will take another look then if nobody else has finished it.
– Deusovi
May 20 '20 at 16:50

Okay, I think it's about time this puzzle got solved. Here's some really decent progress - pretty sure I'm just missing one part of the puzzle...

First:

As per Hints 3 and 4, there are numbers encoded in the diagram in balanced ternary. This is a number system based on the digits -1, 0 and 1 (as opposed to the standard 0-2 of regular ternary). Using 'N' to represent -1, we can infer up to 2 digits from each of the 3x3 blocks in the diagram.

But how do we read them?

Take the second 3x3 block on the top row for example. If we consider just the black vertical bars in each block and designate the 3 leftmost lines as representing the values N, 0 and 1 (going rightwards), we can read off a balanced ternary value downwards. Here, the number is 010 (see the diagram below), which equates to the number 3.

Likewise, if we consider just the black horizontal bars in each block and designate the 3 lowest lines as representing the values N, 0 and 1 (going upwards), we can read off a balanced ternary value rightwards. Here, the number is 10N (again, see the diagram), which equates to the number 8.

Following this decoding procedure for each of the 3x3 blocks produces a grid of number pairs (or occasionally, a single number or no numbers at all), as follows:

This produces a grid of numbers (most often paired) with values in {1,2,3,4,6,7,8,9} - notably 5 is missing; we will return to this observation shortly.

To verify that this approach is correct there is a useful built-in self-confirmation device here. As per Hints 1 and 2, four columns should yield some kind of 'check' for the data, and must bear some relationship with the 'Z' character in grey on the left of the image. These 'check columns' are columns 1, 3, 5 and 9, in which each row contains (1) no digits, (3) the digit 9, (5) the digit pair 6-9, and (9) the digit 6.

What do we do with this grid of numbers - and how do these columns identified above satisfy the check?

Consider the thus-far-unused portion of Hint 4 ("the colors chosen for the middle squares are not arbitrary") and also Hint 5. The Beatles album 'Help!' has a very famous cover, on which the 4 members of the band spell out letters in flag semaphore with the positions of their arms (albeit spelling out the nonsense word 'NUJV', since 'HELP' - their original intention - was not very visually pleasing!):

This hint about the Beatles album, coupled with the fact that the centres of each 3x3 block are coloured red and yellow - the two colours traditionally used on the flags employed in semaphore to make them more easily visible from a distance - all point towards using semaphore in this puzzle.

And this is why the lack of 5's in the number grid is important - as, also, is the fact that no digit appears twice in the same digit pair. Because:

These digit pairs represent the 8 possible positions of flags in semaphore code. If for each 3x3 block we shade the squares that correspond to their encoded digits, we can then read them using semaphore! The grid with shading looks as follows (each column being colour-coded as per the corresponding colours in the 3x3 key in the top-left - more on that later...):

Note that here I have shaded column 5 in purple, like the other columns used in the check/synchronisation part.

Now we can appreciate the significance of the letter 'Z' to the check/synchronisation columns - as 'Z' in semaphore is represented by flags held in positions 6 and 9... the very combination used throughout column 5, and achievable by combining columns 3 and 9! This serves as a useful indication that we're on the right track here...

The next step is, naturally, to translate this information into letters, producing the following grid:

Here, a lower-case 'z' has been used to represent the 2 check-columns which combine to form a 'Z'.

And it's here that I begin to hit dead ends! There is one more piece of information I am confident as to what needs doing with it:

The use of rainbow colours (as per Hint 8) in the key-block in the top-left corner is a clear indication (I suspect) that columns will need reordering into rainbow order: red-orange-yellow-green-blue. The purple columns here are purely those that were for check/synchronisation purposes.

However, there is something else we need to do before then - as suggested by Hints 6 and 7 - and although I have had several ideas as to what these might be, I have not yet found the correct answer... It is clear at least that we must carry out some kind of substitution on these letters, as there are far too many Z's in the non-check columns to make any sense as it stands purely by rearrangement or anagramming. Here are some of my most lucid thoughts on the matter:

What unused information do we have:

1. In the rainbow key box, there is a further pair of digits encoded using the same balanced ternary as before: 2 (01N, vertically) and 5 (1NN, horizontally). This is the only appearance of '5' in the puzzle, and cannot relate to a similar semaphore output (there is no valid '5' position for a flag). Perhaps it is a small hint that our final message is 25 letters long...?

2. If our intended output is indeed 25 letters long, then with 5 columns of 6 rows to interpret, perhaps 1 block in each column is intended not as part of the message but as a 'key' (Hint 7) which enables us to shift the other letters in the column by that number of positions in the alphabet, and yields a message of 25 letters. However, a first inspection shows this is neither the top nor the bottom row, which would be obvious candidates for this approach...

3. Alternatively, we may be required to use this '2' and '5' in calculating such a set of keys for substituting each column (this is currently where I am focussing my attention after a nudge from the OP in comments).

4. I have also considered the notion that the rainbow colours in the key may be 'doing double-duty', and also acting as a number by which each column's digit should be augmented (e.g. red by 1, orange by 2, yellow by 3, etc.). However, the result of this appears to be just as nonsensical as the data we start with, so this doesn't look promising!

Still trying to find out what 'key' information results in the necessary substitutions to read that final message... but I sense the end is close!

• Nice work Stiv! Almost there. You were correct, there was an error in the original diagram which is fixed. Since you're resurrecting this, I'll add a quick hint...the numbers you found in the rainbow box can be combined to determine keys for Caesar ciphers on each column. Thanks for having a look! Dec 28 '20 at 14:03
• @JeremyDover Brill, I'll correct my diagrams to fall in line later and have a think about those keys! :)
– Stiv
Dec 28 '20 at 15:02
• @JeremyDover Just returning to this one again, wondering if fresh eyes help... Question: Re the numbers encoded in the 3x3 box top-left, could this be rot13(n yvax gb 'svsgl-gjb', fhttrfgvat n pbaarpgvba gb JRRXF bs gur lrne, naq guhf Pnrfne fuvsg xrlf qrcraqrag ba FZGJGSF be WSZNZWWNFBAQ va fbzr beqrevat/fhofrg?)
– Stiv
Apr 20 at 9:25
• That's getting closer, Stiv. Remember your next step is to find a key for the Caesar ciphers on each column...maybe Sgt. Sequence could help you out. As an additional hint, the synchronization columns have served their purpose, and can be discarded at this point. Your #3 is the right starting point. Apr 20 at 12:13
• @JeremyDover Okay, thanks - that's some food for thought. I'll let the cogs turn a little...!
– Stiv
Apr 20 at 12:16