Wrap-up: The Making Of "Let us all join the party for hope!"
This is not a solution to the puzzle, but provides notes from its poser. This type of answer has been approved by the community.
Caution: This post may contain spoilers.
0. Where there is save data, there is hope
I had the idea to make a Danganronpa-themed puzzle about a couple of weeks ago, when I realized the release date for Danganronpa v3: Killing Harmony was drawing near. (At about the same time, I clued the words hope, peak, academy in our chat game Cryptic Clue Chat Chains)
I wanted to make a Chiaki puzzle from the start, especially since it would naturally be video game themed and I like video games. And the character is awesome too... I think. But then there were so many characters with so many different abilities, I realized this would be a great opportunity to make a lot of differently-themed puzzles yet tied together by the game where the characters came from. Of course, I couldn't do anything too involved, since I only had a limited amount of time to get the puzzle out before the game release, so it had to be just a series of bite-sized puzzles.
So if I was going to make a video game puzzle, I had to pick a game. I wanted this to be fair to non-gamers, so my first instinct was to pick something that the whole population would recognize, but I soon realized this was quite limited to Tetris and Mario (and maybe a few others like Sonic and Zelda). So instead I decided to go with something slightly lesser known, but make it as obvious as I could. I went with Puyo Puyo as it is a well-known Japanese puzzle game, and I used Arle Nadja's spells as words in the hope that they would be at least easily googleable (I am sorry for forgetting about Diacute!). For a bit of trivia, Arle's first game was released in 1989, which means she has actually been around for longer than Sonic!
Fitting all that was harder than it seems. Initially I just tried to divide all letters mod 5, but some groups end up with no vowels and then fitting words is a pain, and when you succeed sometimes you get obscure stuff such as "percoid". In the end, I gave up on trying to have a nice rule for letter division and settled for a program that given a Puyo Puyo chain, would try to fit in simple words to form it, with a pangram to give the letter assignments. I had to try a few times because having letters from the answer too close to each other restricts the placement too much, as does having an even distribution of colors, which is why the final board has far more purple than red or yellow. In the end, I don't think the answer is immediately apparent from looking at the 6x6 grid and all of the subpuzzle answers are common, so it was fine.
The quote that makes this title is from The World God Only Knows (an anime that, while leaving me slightly annoyed for not having a proper ending, is actually really funny), and I thought it was really fitting given the hope + video gaming aspect of this puzzle.
1. Sorry! I'll try to be useful this time! / 3. Life's a gamble / 6. There's more than one way to win a game
The decision to make all puzzles based on games had the somewhat unfortunate consequence of making this more knowledge heavy than I would have hoped; many of the puzzles are unsolvable if you can't tell which game they came from. The flavor texts for all puzzles had a definition or phrase related to the answer, and for some of them, including these, I added a few additional hints to help narrow it down. I wish the fact that they were all playing a game and that identifying such game would be key had been put in a more obvious way and I hadn't needed to restate that in a hint, but I'm not entirely sure how.
The game picks themselves were all just based on character talent, so not much to talk about here. One other choice I considered was Monopoly for the Ultimate Affluent Progeny, but I couldn't make a decent puzzle out of that.
2. The worst of times are when photographers capture their biggest smiles
This one was hard to think about. What sorts of playful things can you do with photographs? The only one that came to mind was playing "spot the differences", so I decided to adapt something similar to that.
My drawing skills are terrible, so to get similar images I had the idea to take several pictures from the same place from slightly different angles. I tried taking a few from the Art Gallery in Downtown but I feel that Koizumi would have been offended if I posted any of those, so I turned to looking for pictures on the net. Because I wanted multiple pictures of the same thing, it had to be a landmark, and because this puzzle was too weeb already as it was, I picked the Church of Saint Francis of Assisi (which I guess is more of a landmark due to the surrounding scenery than due to the church itself).
I had the idea of using a barcode pretty early on, but I wasn't going to force solvers to check 441 images. I could have used a smaller code such as Data Matrix, but then the solvers would hate me both for making them look through 100+ images and using a weird barcode format. So I came up with the coordinate system as a potentially abusable but not nearly as infuriating middle ground.
An easy way to do the checking is to put the squares over the corresponding spots in the original picture -- you need to scale them down slightly for them to fit, but the wrong images should stick out pretty clearly. Anyway, both solvers ended up solving this just by flipping until the answer came out right: I'm slightly annoyed that they skipped a step, and slightly relieved that the lack of a confirmation of which images are correct didn't deter anyone.
The quote for this title is from Ace Attorney. Except they were talking about lawyers, not photographers.
4. I Squeezed The Baby Out But I Don't Know Who The Father Is
"Am I supposed to know the names of random lolis?" -- IRL friend after reading through the puzzle set
Oh, this puzzle... After remembering Sayaka and her talent, I think this summarizes the thought process behind it:
Of course, after I decided to have an image full of idols, I remembered it had to have an actual puzzle behind it or my plan would have been foiled. After identifying the pictures, this would be basically a bunch of strings which formed a mini metapuzzle of sorts, so this was actually a relatively unconstrained choice. Japanese numbers made this section even more weeb and being mostly single syllables, seemed like they would be reasonably easy to find.
Having written the expressions, I turned to picture selection. A problem here is that my knowledge of idols is not that extensive -- apart from having watched both seasons of Love Live!, not knowing Japanese means all I know about them comes from the dark corners of Dailymotion -- that means a bit from AKB48 (that is three links, by the way), and a smaller bit from others such as Nogizaka46 and Morning Musume.
Only being able to pick names with numerals turned out to be slightly more restrictive than I anticipated too -- for instance, this outright eliminated all characters from Love Live! except for Nico Yazawa, which is the one I like the least (half of her lines in the show are lies and the other half is "nico nico ni", so eh.) If I had a free choice I would have gone with Maki, but she is blacklisted here because her last name Nishikino has both "ni" and "shi", as did some of the other names I looked up. Others such as Miku Hatsune, Misa Amane, Tomochin (Itano Tomomi), Mayuyu (Watanabe Mayu) and Misa Eto were blocked for having no numerals at all.
I began to pick from the more restrictive numbers, which means I started with 5. I needed to pick three, and I only had four choices according to Wikipedia -- Kumiko Goto was a natural choice for the cut both for being retired from the artistic career for a long time and for sharing her last name with Maki Goto, and I figured it wouldn't be fun at all if two of the people selected had equal names. For this selection Maki Goto looks cool, though I have to say I'm not a big fan of Ai Kago, who was just too young (unlike what is implied by the quote that starts this section, I am not a lolicon :) ).
Seven was a similar situation: I could pick between Owada Nana and Okada Nana, and I went with Okada since she has not graduated yet.
The choice for one was only barely less restrictive -- I believe at the end I had only 3 choices to fill the single spot. Sayaka Ichii has, like Kumiko Goto, not been an idol for some time and is now a television personality instead. Of the other two, I didn't pick Ichikawa Miori because other reasons missing, I preferred to not have a name starting with "ichi" (that, and I liked Mion Mukaichi's stock picture better).
For two, one may realize I purposefully only picked fictional characters, mostly for variety. Nico Yazawa was for the obligatory Love Live! member, Eri and Minami to represent what was maybe the original virtual idol group in The Idolmaster, and Sonika to represent vocaloids in the absence of Miku.
Four, on the other hand, is a selection nightmare because so many names contain "shi". The choices were practically endless -- off the top of my head and in AKB only I could list Paruru (Shimazaki Haruka), Yuko (Oshima), Takamina, Yukirin (Kashiwagi Yuki), Sasshii (Sashihara Rino)... However, because of the couple of members of AKB I was forced to pick for the earlier numbers I didn't want to pick more than one member here, so I went with Minegishi, who is who I'd pick if I had a single slot for AKB. In case you're curious, I listed the others in the order I would have added them if I had extra slots, and now that I did so I kinda wish I had one more slot :)
Therefore also for variety, the remaining slots went to Nogizaka46 members: Shiraishi and Kashiwa for being the two having "shi" in their names. Not too unhappy about Shiraishi being here, for being one of the most notable of the group (and undeniably pretty). I would have picked Nishino Nanase for the second spot, but I couldn't because it starts with "ni".
I didn't want the decision to use numbers to be completely unhinted, so I remembered that a large number of songs begin with some form of counting (such as "one, two, three, go!") This would double as both an excuse to make the flavor text be a line from a song and a legitimate hint, and surely enough the song I was listening to (for inspirational reasons?) when making this puzzle, Heavy Rotation, did start precisely in that way, so I went with it.
The title is the name of a "hit" song in Danganronpa, which (fortunately) we never got to hear in the game.
5. All you have to do is cross out the wrong words
Writing Prodigy is a rife theme for puzzles, since it means that I could include basically any word puzzle / game in this slot. A riddle is the most obvious choice, but I'm not at all a fan of those. Crosswords are the second obvious choice, but I didn't deem my English good enough to try making one. So eventually, to follow the tone of simplicity, I picked a simple word game. As a side-effect, this became a nice entry point for the whole puzzle. I didn't realize people would be confused by the red numbers, otherwise I would have taken them out.
To get the word set, I again wrote a program that basically guessed random words and printed when "dirty" was the only consistent possibility after less than 10 guesses. I confess I didn't check whether any words could be removed, but for instance removing "spite" allows "stoic" as a possible alternative answer. Numerically speaking, "1" clues are the least helpful, but I personally found out that the right word jumped at me much faster when I used "1" clues as opposed to "2".
7. Problems that cannot be solved do not exist in this world
Chihiro was an obvious pick for this puzzle, both because of the added variety and because Stack Exchange is a very fitting setting for a programming puzzle. Not surprisingly, a bunch of people tried this one first, though it is a bit more involved than it looks at first glance and requires some basic number theory, which is why I'm not surprised Wen ended up solving it first.
Well, programmers play around in a lot of ways, and most of them involve writing simple programs in the most ridiculous way possible. I have to thank misof for the idea to write a ridiculously inefficient Euler totient function. The numbers in A are very easy to factor, so any reasonably decent algorithm would finish instantly. t() is neither reasonable nor decent by any standards, though.
For the second part, you had two choices: either notice that the sequence is cyclic or compute the recurrence using matrix powers. The matrix approach is definitely more practical for larger modulos, but for a small modulo such as 26, the first option is much easier as the cycle is very short.
The quote from this title is from Haruhi Suzumiya's Yuki Nagato, who has an... over the average skill with computers.