Time to Hit the Bricks!

Question

^{An entry in Fortnightly Topic Challenge #24: Grid-Deduction...}

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It's 2am. The phone rings.

You answer it and are immediately met with an onslaught of franticness from your (in?)famous uncle—a games and puzzles creator of dubious skill and legendary absentmindedness. You realize that, other than a rather interesting New Years card a couple weeks ago, you haven't heard anything in over a month from him, but now he seems to be trying to make up for lost time by cramming three weeks' worth of words into 30 seconds.

When you finally get him to slow down and start from the beginning, you get at least a little understanding of why he's calling—he needs your help—but the what is still baffling. It seems your uncle has gotten himself into some trouble with some, er, "investors," who are now rather (gun-)pointedly demanding their money back, and it's no small sum either. Fortunately, he's got a bit of a stash hidden away. Unfortunately, for you, it was going to be your inheritance; but now . . .

He's about to tell you how to get the money when you stop him:
  "Aren't those investors listening in? You'll be telling them right where you keep your cash!"
But you needn't have worried; your Uncle has, of course, hidden and safeguarded his money, and besides, he's not going to tell you where it is; he's already done that, in a letter he hid away in a book about pirates, right there on your bookshelf!

A few final details settled, your Uncle bids you good fortune in retrieving his (your?) fortune, urges you to come as quickly as you can, and hangs up. You reach for the book on your shelf and shake it to find an envelope bearing your Uncle's unmistakable handwriting, containing two sheets of paper.

The first is a letter written by your Uncle, with some additional information printed on the reverse side:
 
 

The other sheet bears the promised map on one side (not reproduced here, lest the "facility" start getting unwanted visitors), and a diagram of a maze / grid thing on the back:

 

Text Version of the Grid
_{[Alas - there seems to be no way to reliably do monospace fonts in MathJax. Text version of the map grid is thus no longer hidden behind a toggle button, and is now just a plain text blob.]}

 X X X X X X X X X X X X X X X X X X X X X X X ^ X X X X X X X X X X X X X X X X X 
 X   :   :   :   :   :   :   :   :   x 0 :   :   :   :   :   :   :   :   :   :   X   1
 X - x x x x x x x x x x x x x - x x x x x x x x x - x x x x x x x x x x x - x - X 
 X   x   x   :   :   :   :   :   x   :   :   :   :   :   :   :   :   :   :   x   X   2
 X - x - x - x - x - x x x - x - x x x - x - + - x x x - x x x - x x x x x - x x X 
 X   x   :   x   x   :   x 1 x   :   :   x 1 :   :   x   x   :   :   x   :   x   X   3
 X - x x x - x - x - x x x x x - x x x - x - x x x x x - x x x x x - x - + - x - X 
 X   x   :   x   x   :   :   :   x   x   x   x   :   :   x   :   :   : 0 :   x   X   4
 X - x x x - x x x - + - x - x - x - x x x - x x x - x x x - + - x x x x x - x - X 
 X   x   :   :   :   :   x 1 x   :   :   :   :   :   x   :   :   :   :   x   :   X   5
 X - x - x x x x x x x - x x x x x x x - x x x x x x x x x x x - x x x x x - x - X 
 X   x   :   x   x   x   :   x   x   x 1 :   :   :   :   : 1 :   x   x   :   x   X   6
 X - x - x - x x x - x - x x x - x - x x x - + - x - + - + - x x x x x x x x x - X 
 X   x   x   x   x   x   x   x   x   x   :   :   x   :   :   x   :   :   : 1 x   X   7
 X - x - x - x - x - x - x - x - x - x x x x x - x - x x x - x - x x x x x x x - X 
 X   x   x   :   :   :   :   :   :   :   x   x   x   x   x   x   x   x   x   :   X   8
 X - x - x x x - x x x x x x x - x - x x x - x - x - x - x - x - x - x - x x x - X 
 X   x   x   :   :   :   :   :   x   x   x   :   :   :   :   :   :   :   :   :   X   9
 X - x - x x x - x x x x x x x x x - x - x - x x x x x x x x x x x x x - x x x - X 
 X   x   x   :   x   :   :   :   :   x 1 x   :   x   :   :   :   :   :   :   x   X  10
 X - x - x x x x x - x x x - x - x - x - x - x - x - x x x x x x x x x x x - x - X 
 X   x   :   :   :   :   x   x   x   :   :   x   x   : 0 :   x   :   :   :   x   X  11
 X - x - + - x - + - x x x x x x x x x x x x x x x - x x x x x x x - x x x - x - X 
 X   :   :   x   :   x   x   :   :   :   :   :   :   :   :   :   :   x   x   x   X  12
 X - x x x - x - + - x - x - x - x x x x x x x x x x x - x x x x x x x - x - x - X 
 X   :   :   x 1 :   :   : 1 x   :   x   x   :   :   x   : 1 :   :   :   :   :   X  13
 X - + - + - x - x x x x x - x x x - x - x x x x x - x - + - x - x x x x x - x - X 
 X   :   :   :   :   :   :   :   :   x   :   x   :   :   :   x   :   :   x   x   X  14
 X - x x x x x x x - x - x x x - x x x - + - x x x - x x x x x - x x x x x - x - X 
 X   :   x 0 x   x   x   : 0 x   x   :   :   :   :   x   :   x   :   :   x   x   X  15
 X - + - x - x x x x x x x - x - x x x - x x x - + - x - x x x - x x x x x x x - X 
 X   :   :   x   :   :   x   :   x   :   :   x   : 1 x   :   x   :   x 1 :   :   X  16
 X x x - x - x - + - + - x x x - x - x x x x x - x - x x x - x - x x x x x x x - X 
 X   :   x   x   :   :   :   x 0 x   x 0 :   :   x   :   :   :   :   :   :   x   X  17
 X - x x x - x - x - x - + - x - x - x - x x x - x - x x x x x x x x x - x - x - X 
 X   :   :   x   x   x   :   :   :   x   x   :   x   :   :   :   :   :   x   x   X  18
 X - x x x - x - x - x x x x x - x x x - x x x - x - x - x x x x x x x x x - x - X 
 X 1 :   :   x   :   :   x   :   :   :   x   x   x   x   :   :   :   :   :   x   X  19
 X - + - x - x - + - + - x - + - x - x - x - x x x - x - x x x x x x x x x x x - X 
 X   :   x   :   : 1 :   :   :   x 0 X   :   :   :   x   :   :   :   :   :   :   X  20
 X X X X X X X X X X X X X X X X X ^ X X X X X X X X X X X X X X X X X X X X X X X 
    1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17  18  19  20    

 

You start to study the grid, wondering just how to fill it all in.

You recall your Uncle's parting words:

"Remember - when you're done with everything my instructions tell you to, your last step will be to find a final, common four letter English word. You'll know what to do with it when you've got it.
And.... Hurry! These guys aren't big on patience and I really need that cash!"

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What to do:

• Fill in the grid!
• Find the passcode!
•   ? ...
• Find the final word!
• Get the money!
• Save your Uncle!!

_{By the way, I put in a bit of effort to make this puzzle work in stages. I think it will be a lot more fun for solvers if they work through it in its entirety on their own, so - if partial results are posted, please consider NOT looking ahead of where you are unless you really are stuck!}

 

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Think you're done?

Find out if it's time to show you the money!

Cipher text: NBif mFJocz kDxCOm ko
Key: ####

$ $  

Answer 1

Fill in the grid!

The grid can be solved by finding paths of length 3 with no branches that start from a dead end. No matter which state is assigned to the first tile of that path, the third tile will always be the same state. Already solved tiles do not count as branches. Repeatedly using this rule leads to (red = 1, black = 0):



Step-by-step solving of the bottom left:
1. Initial layout of the bottom left.
2. From the dead end at the top left we can find three paths of length 3 (blue). The first one of those can be solved because the top right and bottom left tile of the 2x2 have to be the same state (they have the same neighbours).
3. Starting from the tile above the end of the second path, it is now possible to fill in the whole left part.
4. We can now find a new path starting above the 1 and then two other paths around the just solved tile.
5. We know again that two of the corners of the 2x2 at the end of the last path have to have the same state and can thus deduce the bottom right of this 2x2 to be activated. Working backwards we can fill in all the remaining tiles.

Find the passcode!

Converting the coordinates to 0/1 and converting the resulting binary number to ASCII gives the passcode XgcXu which gives us more instructions at https://i.sstatic.net/XgcXu.png

? ...

We have to find a path through the maze according to the rules. Blocking of dead ends and parts where you have to walk through the same state 5 times in a row repeatedly gives the following path:

? ...

This gives us the path: RRLLRLRLLLRRLRLRRLRRLLRLLRLR
28 turns in total with 14 turns each ready to be used in the Vigenere cipher. Using the keys twentyeight and fourteen yields (thanks Hakdo):
STACK IMGUR JPG
LOWER JUS +
UPPER(PX)
which leads to https://i.sstatic.net/jusPX.png

Get the money!

This tells us to use the Bacon-Cipher on the path through the maze interpreting 0 as a and 1 as b which gives us:
Follow the yellow
Combined with the title of Time to hit the Bricks this is clearly a reference to The Wizard of Oz. The full phrase is Follow the yellow brick road and because our uncle tells us that the last step is to find a final, common four letter word, we use the keypad to insert road which corresponds to the following keys:
7623
Converting the number to Roman numerals VIIDCXXIII and using the Vigenere Cipher again on the verification cipher gives:
STac kIMgur pVpZMp ng
which leads to https://i.sstatic.net/pVpZM.png

Save your Uncle!!

With the safe open it is time to grab the money and decide whether you prefer your Uncle or a fast inheritance.

Answer 2

So far w l has:

found the path through the energy field, but since the codes has proven too much for them, I think I'll help here. Apply the three keys (not as digits but as spelt-out numbers) to corresponding ciphertexts to get:

STACK IMGUR JPG
LOWER JUS +
UPPER (PX)

So next step is

https://i.sstatic.net/jusPX.png

Which wants that path to be interpreted as Baconian ciphertext. Specifically, active cells as B, inactive as A, i=J and U=V. Decodes into:

Follow the Yellow