(Thanks to f'' for the help in chat! He solved the majority of this puzzle - I just came in at the end.)
Step 1: Crossword
The crossword was solved by feelinferrety, Z. Dailey, and Sleafar:
Step 2: NOTHEX
Step 3: Using The Key
you get a message for all four paragraphs:
Step 4: Following Directions
Step 5: The Image
Step 6: Interpreting Everything
Disclaimer: This is only posted in a half-serious manner because I was bored and looking for alternative decodings.
The message was sent by:
The first trap is the simple answer (given by Joe).
If Sarah sees him ask Anne out, she knows he fell for this trap.
The second is far more convoluted. First we take the numbers in
54 46 65 59 ...
Her name is
Her phone number is
The translated message is:
Which, converted to plain text is:
The result above
Translating this, we get:
These are the
Which spells out the following:
Which are the
Giving us her phone number:
Which, pop-culture tells us belongs to:
More partial answer, work in progress:
As noted in Rupert Morrish's answer:
So if we decode the cipher text found above using that cipher and key, we get:
So if we ROT-13 the remaining still-encrypted part, we get:
And.. I'm not sure where to go from there. If I was forced to give an answer right now, I'd guess that
...and that's as far ...
Scroll to the end if you just want the answer. I give a detailed explanation of how I reached it.
First, I hypothesized that the permutation has two cycles: one of length 9, and one length 17. The length-17 one contains T and R, and the length-9 one contains E. How did I get there?
Look at the string JR. at the start of the second paragraph. That's a ...
I'll start with a few simple ones to get us rolling.
Base64 has a 2/3 chance of requiring one or two trailing = signs - if you spot any of these, there's a very good chance you're dealing with Base64 encoded text.
A Bacon cipher is composed of 2 binary bits, which can be represented by anything (eg. could be upper/lowercase as in one recent question, or ...
Here is an answer that decodes this image. Not being a programmer, I used ImageJ and Stegsolve to look at this file.
Viewing with bit0 then bit1 provides these two images:
Then continuing to toggle through bit2, bit3, bit4 provides the following images:
And finally, these images with bit5, bit6, bit7
So the name of the painting is:
This guide aims to explain various ciphers, help you understand how they work, and how to decode them with or without a key.
This answer is currently being split into multiple posts to improve scrollability and readability after some advice from other users. This may take a while, and apologies for the stop-start fashion of it.
Mission accomplished! This ...
The boss has encoded the numbers using:
The numbers are thus as follows:
My contact @hagfy (real name unknown) has identified this as the highly-advanced
...and has used enhanced decryption capabilities to obtain the final location of the anti-shrink device:
The dots and dashes are Morse Code as noticed by @Randal'thor
When it is translated to text it reads as follows:
As a bonus
is Roman numerals for
which was the season and year when the puzzle was posted...
Taking the lines with squares on them, we get this message:
Superscript T has a specific meaning: it's the transpose of a matrix. Assuming letters represent matrices, the bottom three lines can be guessed:
$K$ is [symme]tric
$H$ an[d] $A$ a[r]e [orthog]onal
$I$ i[s the] identi[ty]
The secret of the universe is
Because the famous leader who found the tabelet is
He invented a code named
The message on the piece of paper has been decoded using
so if we use the cipher above to encode it back we get
When we undo what the MAGE has done to it
which again decoded by the cipher of the great leader gives us