Just another day in the Shack

Question

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.

^{Notes - ##TO BE READ##:}

^{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

Answer 1

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'.}

At this stage, we have two outstanding unused pieces of information in the key-block in the top-left corner which together should somehow explain Hints 6-8:

1. There is a further pair of digits encoded here using the same balanced ternary system as before: 2 (01N, vertically) and 5 (1NN, horizontally).

2. The use of rainbow colours (as per Hint 8) in this key-block should likely lead us at some stage to a reordering of the corresponding columns into rainbow order: red-orange-yellow-green-blue. (The purple columns here are purely those that were for check/synchronisation purposes.)

At this point it took a fresh pair of eyes to see what I couldn't (see @richardb's answer, here). What remains for us to do is...

...identify a set of Caesar shifts whose values depend on the hidden numbers '2' and '5' that can be applied to the five rainbow-coloured columns to reveal the hidden message.

It turns out that some pretty nice letters are generated (i.e. not a horrid slew of Q's, J's and X's...) if we shift the first column's letters by 2 places backwards, then each subsequent column by an additional 5 places on top of this (i.e. by 2 + 5(n-1), where 'n' is the column number).

Then once reordered according to rainbow order, the message can be read off backwards along each row and down:

This gives us the final message:

SC SEND SIGNAL FLAKS AND LOO ROLLS EC (where I presume 'SC' and 'EC' represent the radio codewords 'Start/End Communication').

Now move, move, move!

Answer 2

Final parts of the puzzle (standing on the shoulders of giants).

We have the digits 2 and 5 in the key box, which can't be a semaphore indication.
The columns are Caeser keyed, so we'll try an online Caesar solver.

We get best shifts of: 12, 7, 12, 17, 14. Three differences of 5, and for the first column 2 is the second best choice. OK, looks like we're onto something here. Let's go with a shift of 22 for the last column.

Finally let's transpose the columns.

Rainbow order gives us:



Wait, is that an 'AND' backwards, and maybe 'SIGN' as well?

Let's try reading it backwards. Some characters are filler (or possibly initials).

(SC) SEND SIGNAL FLAKS AND LOO ROLLS (EC)

Let's hope they haven't been waiting all this time for resupply!