# Density in Den Sitting

Please find below a word search puzzle. But it's not just any word search...the words you find cannot be too dense. The definition of a word in this puzzle:

1. appears in /usr/share/dict/words:https://gist.github.com/WChargin/8927565 (be aware, this dictionary does include numerous proper nouns, particularly geographic locations, which do count as words)
2. must be at least four letters long
3. appears contiguously in the grid in a single direction
4. does not appear within another legitimate word (note: words that are legitimate both forwards and backwards for their full length [e.g., RAIL and LIAR] are legitimate, but only count once)
5. the average of the letters in the word (calculated A1Z26) can be at most 11

When you have found all 36 words, you will find a clue that you can use to derive the answer to this puzzle, which is a six letter word. I hope you enjoy!

CSV Version:

H,N,N,F,C,O,R,O,L,I,A,J
T,N,E,V,E,L,E,A,C,A,M,D
A,E,I,E,A,E,E,A,C,L,N,N
B,A,A,B,T,P,A,W,I,I,T,O
L,A,A,E,A,F,A,F,H,A,S,P
E,D,R,A,G,B,A,B,U,C,A,M
U,C,E,S,C,S,O,D,A,B,B,M
F,R,A,U,D,A,A,A,P,E,E,D
M,G,A,B,P,A,M,P,E,R,E,D
O,B,D,L,E,G,F,T,M,E,D,E
D,E,T,A,L,U,D,A,C,E,H,I
A,I,E,L,C,U,N,R,R,L,G,T

• This is a really cool puzzle. +1 Sep 30 '20 at 14:54

HELIUM

Here's how we got here, building off of Lukas's answer.

Completed grid:

Reading around the outside of the grid, we see the word NONOGRAM (no surprises here from Jeremy, eh?)

From there,

We take the letters that are left unused from the center 10x10 grid, and use those to create the nonogram. So, reading row by row, we see that the top row has a C and then an A, so the nonogram clue for that row is [3, 1]. Here's the empty nonogram grid:

Completing the nonogram grid gives us this:

Then, we overlay the shaded in squares over the original grid, like so:

This gives us the clue:

ELEMENT WITH SUCCESSOR UPPER LEFT METAL

HELIUM - He (element) + Li (successor) + U (upper) + M (left metal)

SILVER - If you read it as "Element with success" then silver is "with" the element that represents success (Gold) and it's a metal. SODIUM - the word "eleven" is in the upper left of the grid, which is the atomic number for Sodium, an alkali metal.

• I thought it was HELIUM, because its successor is Lithium, the upper left metal. But I didn't feel sure enough to post anything. (I also tried to interpret it as a cryptic clue, with no luck.)
– Deusovi
Sep 30 '20 at 21:54
• Ah, yeah, that's definitely another possible interpretation. Probably better than mine, in fact. I'll edit it into the "alternate answers" section here. Sep 30 '20 at 21:56
• Your answer also makes sense because the puzzle is about density Sep 30 '20 at 21:59
• @Deusovi is on the right track. Recommend trying to read the clue as a cryptic &lit. It was a bit ambitious on my part, given some of the puzzle constraints. But nothing ventured...no one gets a chance to laugh at you on the Internet. Sep 30 '20 at 22:26
• My thought process on wordplay was rot13(UR [ryrzrag] + YV [jvgu fhpprffbe] + H [hccre yrsg] + Z [zrgny]). This did not come out as well as I hoped...neither fish nor fowl. Sep 30 '20 at 23:58

THIS IS NOT AN ANSWER, BUT RATHER SOME NOTES ON THE MAKING OF THIS PUZZLE

@bobble provided the initial inspiration for combining the puzzle, and suggested I write some notes on its creation. Spoilers abound!

The puzzle really only has three performative steps: the word search, solving a nonogram, and then answering a (ultimately not very well executed) cryptic clue. To me, the aha moment was to have the solver realize that there was a nonogram to solve. So I resolved early on to encoded the nonogram clues within the word search.

I actually constructed the puzzle backwards. First came the clue I wanted to embed, so I had an idea of how many characters I needed. I left myself a bit of wiggle room, but ended up not really needing it.

The next decision was how to embed the nonogram in the word search. A thankfully early realization was that you cannot encode it with strings of present/absent letters, since that is the solution to the nonogram. I initially thought of using Roman numerals, but it would take too many characters. I finally settled on using the uncovered letters with A1Z26 encoding. This provided the idea of needing to calculate the density of words, because that let me introduce A1Z26 as a thing.

The next problem is how to differentiate row clues from column clues. I thought about color coding with red and cyan (R and C), but the problem is needing twice as many uncovered letters, making the word search part of the puzzle even less challenging. I decided to try to arrange it so that a single set of letters could encode both the row and column clues. This was not easy, and caused several iterations in puzzle creation.

Ultimately, making the nonogram was trial and error, trying to meet several criteria: the right number of shaded boxes, being able to encode the row and column clues together, maintaining some level of challenge, and having a unique solution. Each of these bit me in the behind on at least one attempt.

With the nonogram in place, about 54 squares out of 144 were now fixed, and it became a question of filling in the rest. This mostly consisted of finding the tightest corners and putting them in words first. Leaving the border free, except for needing 8 squares to encode "NONOGRAM", ended up being my smartest decision...having that freedom is probably what made the puzzle possible.

I then wrote a script which found all of the words through each position, and there were definitely some stray words that this step caught. Usually the fixes were pretty straightforward, affecting a word or two. It also caught the biggest fly in my ointment: in a nearly final implementation, the fixed letters from the message and the nonogram encoding including the word "BABE"...there was literally nothing I could do to remove that except to manipulate the nonogram. But here I got lucky: the two Bs in BABE were probably the only location in the nonogram encoding where I could just switch them to the other corners of the rectangle they made, without disturbing the message or the nonogram encoding. It is much better to be lucky than good.

A final step, which I cannot emphasize enough, is the quality check. I went through the puzzle twice more, from beginning to end, making a wordlist, rechecking the nonogram encoding...ALL of the steps, as a solver would have to. As a setter, it does get tiresome to go through the same puzzle again and again, but it is important in creating a high quality puzzle. You have "guilty knowledge" that you can't unknow, but you have to do your best to approach the puzzle innocently.

• Super fun puzzle, I love the "different puzzle hidden within a puzzle," the first puzzle I made here had the same kind of trick. Thanks for sharing it with us! Oct 1 '20 at 1:04

(Partial) I think the 36 words are

All of these satisfy the given conditions. Also, e.g. in the case of "pampered" and "ampere", the longer word was chosen.

JAILOR
ELEVEN
HASP
DRAG
CUBA
SODA
FRAUD
PEED
PAMPERED
GELD
NUCLEI

BATH
TABLE
FUEL
AREA
LEER
BAST
TIED

TEEN
CLEW
RACISM
BARS
DAFT
AFAR
THEE

BEEF
PEAL
VIAL
FILM
HIND
CRETE
SAGO
BEET
MERMAN

• Weird, I got all of these plus one more: rot13(SUN'F) Sep 30 '20 at 20:19
• @kristinalustig I guess apostrophes can't be dismissed? Sep 30 '20 at 20:24
• @kristinalustig You can use apostrophes where they appear in the puzzle :-) Sep 30 '20 at 20:58
• Looks like a good start! Do you have a line on the six letter answer? Sep 30 '20 at 20:59
• @JeremyDover I'm nearly done I think! This puzzle is amazing. Sep 30 '20 at 21:04