This regular word search requires
The simplest solution would be
Here's an example of such a solution
But, that's no fun and seems a bit like cheating. So, let's restrict it by requiring it to only match one of the words we're looking for.
Honorable mentions (matching multiple):
While a couple words have yet to be found in a unique way, @Sleafar ...
Well, I believe I've found your beautiful BEE! Sorry for being so clumsy!
First, the X can't be a B because of the following chain of deductions where all the numbers are E:
Then the X here can't be a B for almost the same reason:
The X here can't be a B because of the ! - it can't be a B because of !41 but neither can it be an E because of ...
The solution is this path:
The clues that give it to us:
The complete list of connections is:
Here's the spreadsheet where we all figured this out; I've made copies at various times so you can see our progress. Many of the words are also highlighted in the sheet (though I'm sure we've missed some).
Here's my answer:
From this point on, there is no spoiler text, because it makes it easier to format, at least for me.
T E N I N E
F I O N E V
O G X R V I
U H H I E F
R T W O S Z
I started by figuring out the letter density in the overall puzzle. The letters break down as follows:
So it turns out (see comments) that actually there are only 39 names, not 40. Here they are in order:
and they are of course all
and the final grid is
Courtesy of BmyGuest himself, here is the initial grid colour coded:
And step by step, courtesy of Jonathan Allen:
Each characters on the board is:
Now it's our duty to:
Some first steps are:
Then here is the result:
To extract the final answer:
As commented by hdsdv, this is related to above board:
Thus the final answer is:
There is a nice general theorem governing this sort of thing (which I'll give at the end), but here's how to do it from first principles.
I'll assume, for reasons set out in my comment on the original question, that A and B appear independently with probability 1/2 each in each position. The probability we're after will be different if the frequencies of A ...
The rest are here just because I was instructed to add them so the puzzle would be complete.
All credits go to Kruga. I would not be able to find them otherwise.
From the remaining letters you can form:
@Stiv found the final answer, go see his answer for an explanation! The thing you are missing in your crossword is
Now clearly there is something a bit odd about this crossword...
All the words follow a pattern
See Stivs answer for the final step!
The answer to the question of what your crossword is missing is:
A lot of credit for solving the initial crossword and wordsearch needs to go to @BeastlyGerbil (go upvote their answer!) with helpful contributions in comments from @Anthroman, @LannyStrack, @teedyay and @oAlt. The solution details for those are listed in full in BG's answer, with the finished ...
As tradition requires, here's the finished product first. Progress pictures at the end of the answer.
Then, we remove the words from the grid, tighten everything up, and repeat for
Lather, rinse, repeat. Theme 3:
And finally, Theme 4:
Everything below this point is only preserved to show solution progress.
Well. This seems a bit ...
I have found the names, symbols, and atomic numbers for the first 118 elements in the periodic table. $118*3=354$ so I presume these are the "over 300" hidden things mentioned by OP.
I used the small grid with the plain text that I could copy. My search preferred to find items in the top left so, although there could be multiple instances of a symbol or ...
I have found all of the
Up to 118. I presume no more are present. Not sure where the "300" comes from, perhaps there's also something else hidden in the puzzle?
Note: colours are meaningless in my solution pic.
The answer is:
The explanation is:
From there we just apply the formula:
So, for example:
Additional info added by AE:
That's absolutely correct.
For our prisoner to begin deciphering, he just needs to:
I've found up to 27 possibilities so far,
Please let me know if any don't qualify for obvious reasons :)
Also I am done for at least a couple hours, because I've been shirking work for too long looking at this.
Several are also present in @Kruga's excellent answer, but given it's breadth and good formatting, I don't feel comfortable stealing them.