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RESEARCH
Volume 4, Issue 4 - "Getting Pumped" by cake>pie
Probably the most infamous. Requires a ton of re-bonding, space re-usage, and special cases. The sensor helps a bit but the paths really have to be crammed in. Back when the SolutionNet online leaderboards were up, only about 12 people (including the author) beat this one.
Volume 6, Issue 3 - "Catalyst II" by zaq1xsw2tktk
GuavaMoment chose this as a final puzzle for the original 2012 tournament for a good reason - the fusion and fission required to do this puzzle legitimately (without exploiting a bug) are unparalleled, and once again require an incredible amount of space re-usage and special cases.
Volume 3, Issue 10 - "Squaric Acid" by Kanddak
This puzzle seems like it should be relatively straightforward, but it's pretty hard since there's a lot of sub-tasks involved. This ended up being one of the last ResearchNet assignments I solved back when there were only 4 volumes.
PRODUCTION
Volume 8, Issue 13 - "A New Beginning" by Lanky
The math in this one ends up being pretty obnoxious, even if you ignore the random inputs and just use known quantities for everything.
Volume 4, Issue 4 - "Inorganic Pigments" by cake>pie
The outputs here are unbalanced compared to the inputs, so avoiding circular deadlocks or inefficiencies are quite difficult.
Volume 3 Issue 8 - "Nobility" by GuavaMoment
Probably not that hard by today's standards, but it was the first assignment to introduce "sorting by bonds". That paired with tricky nuclear math means getting a good score isn't easy.
HONORABLE MENTION
Volume 8 Issue 3 - "Lies" by Blueeyedrat
Aaargh!
I need to throw in some support for Vol 1 Issue 8 "Chlorination". It looks easy! It's 2 out of 3 difficulty somehow! The math works pretty nice! Then you realize that you can't just split that chlorine down and the limiting factor is that the hydrogen in the hydrochloric acid has to be a hydrogen from the borane. UGH
Also need to show some support for Vol 6 Issue 2 "Deadly Microwaves". I read a story of someone who thought that microwaving plastic wrap would produce dioxins, and once I realized I could fit dioxin in a large output, the design of the challenge was easy. I spent months trying to see if it was possible to solve at all. It felt so possible since the math works out so nicely, but doing it was so beyond me for a long time. I added the beta input just to make life easier for everyone else, and because I was trying to prove it was solvable it since I needed it for the finals of my tournament. I'm honestly surprised both finalists solved in in the two weeks (I think?) I gave them.
In my opinion, based solely on how much time I spent solving it, the three hardest challenges in increasing difficulty are Getting Pumped, Catalyst II, and Deadly Microwaves.
https://youtu.be/al1F1b5XFZA?t=624
(spoilers on how to solve Catalyst II, of course)
Basically, the "input fusion" bug allows you to input a molecule on top of a single atom, then fuse that atom into the just-inputted molecule on the same cycle, resulting in no collision at the end of the turn (and allowing fusion into atoms that would normally be completely surrounded).
BTW, I've just solve that puzzle without cheating. Amazing experience)