Combining Rate and Instructions to Create Beautiful Madness
Let’s hop back into the deep end of Opus Magnum optimization. We’ve talked about rate before, also called throughput. This is a way of scoring machines where there is no need to start outputting quickly, merely to reach a steady state that outputs as often as possible. We have also talked about instructions, and how to build solutions with a small number of them. Now it’s time to make rate-optimal solutions with as few instructions as possible. Or as the Opus Magnum community calls it, RI.
Along the way, we will dive into some of the more creative tech that the community has used to achieve better scores here, and look at the results from the two tournaments which have featured RI optimization. But we must start simpler.
The Basics
Fast solutions need to take their inputs quickly. With rate optimal solutions, this becomes a strict requirement to grab an input every 2 cycles. This in turn implies at least 2 arms grabbing each input, so that they can take turns grabbing. Face Powder from chapter 1 shows this principle:
It also shows another principle: hex arms are very powerful. No reset is needed, so you save instructions there. And what’s more, the hex arm lets your inputs take a ride around the loop as long as they need, often passing over several useful glyphs in the process. The programming for this solution shows how it reaches this steady state:
There are 3 instructions on each arm, plus one usage of the clock instruction to force the machine period to be 4 (rather than the 3 it defaults to when every arm has 3 instructions). The clock is never counted as an instruction.
The second arm doesn’t start right away, it waits until it can synchronize its own steady state behavior with arm 1’s.
As this machine makes an output every 4 cycles, it is min rate. Scored for RI, it has 6 instructions, which is also provably optimal. But not all puzzles have the chance to reach that pinnacle of optimization. Let’s look next at Refined Gold.
Problematic Periods
A rate optimal Refined Gold solution makes an output every 10 cycles. Where we were able to make a period 4 solution before, it now seems like the ideal period is 10. But if every arm has to stay busy, and nothing can loop until it has done 10 cycles of action, we write quite a few instructions:
What’s more, with 10 instructions for a loop, the ordinary 4 cycle loops don’t even divide evenly. Extending the period to 20 costs more instructions, so we do something else. We place 3 arms to do the 5 quicksilver transfers, two acting twice and one acting once. In the screenshot above, we write 23 instructions to solve Refined Gold with optimal rate.
A few tweaks to the above to use more hex arms leads to a lower instruction count of 19. Hex arms do have the problem of grabbing things that need to stay dropped, so this iteration also requires two separate projection stations and a longer travel time for everything.
Once it hits steady state though, it is optimal throughput just the same:
However, wouldn’t it be nice if period 4 worked anyway? Then arms could stay busy without needing duplicate instructions.
Making Period 4 Work Anyway
Historically, the first period 4 solutions to Refined Gold at optimal throughput used a track loop. This resembles techniques from raw instruction optimization. If you want to do something on some tape loops but not others, make the end position of the arm different from the start position.
The quicksilver is no longer awkward at period 4. Those two little arms just have 4 instructions each and repeat naturally. The lead becomes awkward, and the track loop solves that problem. The big V shaped track loop has 10 segments, and both of the hex arms have grab-plus-drop-plus as their programming. Across 5 tape loops (20 cycles), each one moves the metals a single time, then spends the rest of the time returning to where it started.
In effect, the above period 4 machine is just a period 20 machine whose programming is 5 copies of the exact same work, so only needs to be written once.
It got better though. panic found this 12 instruction solution with 3 projecting arms, taking 120 cycles to loop through steady state. It uses input suppression to put whatever is held back on top of the lead input, and only grab a new lead if the gripper was emptied by outputting gold.
Many of the 9i candidates ended up accidentally putting a quicksilver back on top of the quicksilver input, sacrificing a small amount of rate. But 6 months after the above, huetobi found a working 9i:
Interleaving two hex arms gives the needed geometry. To handle the case where a gold atom won’t project any higher, it places an extra projector right after the input. After gold is exchanged for lead, that projector takes the quicksilver which would otherwise be placed back onto the input. This was a huge triumph, as now Refined Gold had also reached its limit.
Not all puzzles are this easy – these have been the first two chapter 1 puzzles. What comes up when you go to journal monsters? Or tournament monsters?
Sailcloth Thread
We saw an easy puzzle with 4r, and a slightly more challenging one with 10r. But 10 is nowhere near the most problematic value we will see for rate. Sometimes rate isn’t an integer. Every 8 cycles in Airship Fuel, you need to make 3 outputs. One iconic example of a fractional rate puzzle is Sailcloth Thread. It’s an infinite chain output, so rate counts the speed of adding new monomers instead of dropping outputs. If you build the chain at “almost top speed” you get 4r:
If you don’t mind using an entire hextant of space, you can do some swinging and get that down to 17 instructions:
But there’s a problem. Your inputs have 4+1 = 5 atoms, while one monomer of the product has 9. If you make two sets of inputs equal one monomer, you waste something. In the first gif, the earth atom is only pulled one time per 4 cycles. In the second gif, there is a salt dropped into disposal every 4 cycles.
Actual min rate for this puzzle is 3.6r. 10 monomers every 36 cycles.
90 Atoms at a Time
Madmaster5000 was the first to put together a period 4 solution at 3.6r. His solution took 83 instructions, and built 90 atom blocks:
RP0’s reaction sums it up best: chicanery.
Madmaster kept going. He turned the 90 atom constructions into 81 + 9, making the intermediates less squiggly and saving a chunk of instructions. This design is 50:
In both of these designs we see “wands”. These are arms which have grab but no drop. The atoms they hold only serve the purpose of bonding and unbonding things in flight. At period 4, wands allow 3 consecutive useful actions while any arm that has grab and drop only gets 2 other useful actions. By removing the drop, these arms also just save an instruction outright.
To set up wands, Madmaster uses really long one-way tracks. An arm grabs the input and moves forwards on the track. The next time through its instructions, it moves again. Along the way it debonds pieces of its structure wherever is appropriate for the eventual wand arm to grab it. Dozens, sometimes hundreds of tape loops later, the wand arm does its grab, never to let go. Come steady state, the one-way tracks look decorative, but they spell out the journey of one lonely arm.
For 6 months, this was the record, until Madmaster returned once more, claiming the 50i solution “looked too sane”. This is 39 instructions:
This led to the term “Sailcloth Valley”. It evokes both the Valley of Despair from the simplified Dunning-Kreuger diagram, and Uncanny Valley from an appearance that is close to but horrifyingly different from the norm. We’ve learned that we knew too little about the solution space, and the solutions that taught us this are monstrous.
With this puzzle and the groundbreaking designs, Madmaster showed a core principle of RI optimization. You don’t need to do the least amount of work to get the job done. You just need to engineer a situation where some number of instructions can do an unbounded amount of work. The large 90 atom chains are trivial to turn from arbitrarily bonded earth atoms into the actual output, because bonding and calcification glyphs don’t cost instructions. Reshaping a large molecular structure is a cheap operation because wands exist. If you can get from inputs to something cheap to do unbounded work to, you’re most of the way there already.
Along came rebix
The current Sailcloth Thread RI record is lower still, at 33 instructions. It was made a few months after Madmaster’s 39, by rebix who has emerged as the top Opus Magnum player of the current era.
His biggest improvement was making the core design look like the 4r solution from before, but with wands to allow rotation on consecutive cycles. With that change, the solution could afford to have an additional wand arm come in at the same time as the double monomer to perform another wanded rotation, making space for the extra atoms without interrupting the movement from the main pipeline. The movement on 6 consecutive cycles as the spare monomer enters the chain is tight, but valid.
One hex arm delivers all of the wands needed, leaving its long one-way track smeared about the playing area. Despite the daunting rate of 3.6, it has become almost comprehensible at the hands of good tech.
The timing of this record was (by no coincidence) the exact same week that everyone involved with the Opus Magnum tournament was optimizing Critellium.
Critellium and the 2024 Tournament
I stopped my short lived tradition of annual tournament recap blog posts in 2024. I hope to partially remedy that here. Instead of a computation puzzle, Zorflax’s tournament ended with a normal (but extremely difficult) metals puzzle. For scoring, he gave us the choice of our favorite 2 out of 3 metrics. Each submitter would be ranked in all 3, but only the top 2 placements per person would actually count towards tournament scores (so we could slough a metric if we didn’t feel inspired to do it). Two of the metrics were TI and Sum, community metrics which by this point were standard fare in a tournament. The third was RI.
We knew RI had the potential to be a huge design space, but Critellium was built to make it even more complex.
Courtesy of the mixed purification and projection paths to get from input to output, 136 inputs can make 15 outputs. RI had to account for a 272 cycle steady state in an instruction-efficient manner. TI and Sum were allowed to just throw atoms away if they caused problems, but RI needed to use all of them perfectly. That meant:
- 136 lead purifies to 17 copper
- 136 tin purifies to 34 copper
- 136 iron purifies to 68 copper
- 58 of the 119 copper purifies to 29 silver
- The other 61 copper project to 61 silver using 61 quicksilver
- 45 of the 90 silver project to 45 gold using 45 quicksilver
- The remaining 30 quicksilver bond directly into products
Forget counting 90 basic earth atoms at a time, we had to count these portions out exactly.
My thought process
I noted that 272 was at least a multiple of 4, so period 4 would be the obvious period choice. Every lead, tin, and iron had to be purified, and purification at period 4 is a well studied problem. Purified gold gives an example in its RI record:
Period 4, most purifications are done with hex arms, the larger the value of the metal the more tape loops between times it has any action.
In Critellium, once you make copper, that’s when the counting begins. Up to that point, it’s basically just a more complicated purified gold where you end up making 7 copper for every 8 quicksilver.
So I designed something that made bricks of copper and quicksilver, and started there. Here is 55 instructions spent on the “easy part”:
During this entire portion of the machine, it is illegal to spend quicksilver. You cannot use it to project any lead, tin, or iron, because doing so will equate to missing some value. So it has to just exist, and that is best done by using it to provide structure to the rest. With a huge quicksilver backbone, I make a conveyor belt for the copper. The too-early copper atoms that aren’t synchronized with the others turn into a big smear of one way track that serves as a wand in steady state.
Counting is easy, portioning is hard
This machine makes one brick per 16 cycles. But the final design will need to make 15 outputs per 16*17 cycles. So every product requires 17/15 bricks, until we have processed 17 bricks and can loop.
Counting to a large arbitrary number like 17 is best done by building a stick and grabbing at the far end of it. If the grab fails, you don’t have 17 things yet and the stick builder adds another. If it succeeds, you are ready to process.
But how to actually process a 255 atom object that is 17 copies of a 15 atom object, into 15 copies of a 17 atom object? That sounds like a hard task of portioning the atoms! Thankfully, you don’t need to. Both copper and quicksilver have the same role: upgrade copper to silver. If I can just make a module that will blindly receive either copper or quicksilver, and function identically in either case, I don’t have to do the hard part.
So what I did: Use a wand to steal 2 bricks. The wand is on a 136 track loop and advances 2 times every 4 cycles, so it needs 272 cycles to finish its loop. That synchronizes it with the desired machine period. Over the course of its lengthy journey, it converts its two bricks into a 30 atom line with 14 copper and 16 quicksilver in an effectively random order (whatever is most convenient).
Then it dropped this stick off at a station capable of grabbing an unknown atom and a copper, and using the unknown atom to upgrade the copper to silver. Portioning problem solved! Timing problem created.
Synchronicity
There was a new problem. 2 out of 17 bricks were stolen by the wand, so 15 out of 17 went into another period 4 mechanism which would turn them into almost-critellium. And these had to meet up perfectly at the upgrade station. If the missing bricks arrived at different times, the upgrade station would crash.
It takes a pretty long time to straighten out the 2 bricks into a line, so I needed the other process to take a while, but at some point extra stalling means extra instructions. My best option turned out to be using a single arm to steal away one extra brick, at the cost of 2 instructions. A grab and a track movement. The 16 cycles spent making the machine wait for one more brick, solved problems that cost way more than 2 instructions to address elsewhere.
In the end, I had this 134 instruction monster:
The lower half of the machine gets four tape loops (16 cycles) before the next brick comes in, so many of the arms get to be on tracks and perform longer operations more gradually. In that respect, Critellium was slightly kind. Optimal rate was 18.133r, larger than 16, so at period 4 you could do 4 entire tape loops between outputs and still have downtime.
How did other players approach the puzzle, and how did 134 instructions stack up?
Results
Somewhere inside this 9 hour video are all of the submitted solutions to Critellium. Being a complicated puzzle, and having each player submit up to 3 solutions, this was a marathon for the results team. Zorflax and mr_puzzel and I stuck around the whole time to talk about what was on screen.
18 players made optimal rate solutions. Of those, the highest instruction count was over 20,000, from AGrapeJellySingularity who felt like optimal rate at period 272 was good enough. That certainly allows you to do the counting and portioning the simplest way – in the instruction tray. But holy cow that’s a lot of programming.
Some people used period 16 or period 8 to give a little more flexibility than going down all the way to 4. The best scoring of those was fiesta0618, whose 5th place solution at period 8 had 262 instructions. Then the top 4 were the most optimized efforts.
4th place was Madmaster5000, the very same player who drove us into Sailcloth Valley. His solution had 161 instructions and employed multiple counting sticks:
This really demonstrates the principle of “build a long stick and then try to grab at the end”. After a bunch of counting and merging, all of the proper purifications and projections are complete and the sticks consumed on the right side have 45 gold, 45 silver, and 30 quicksilver. His outputs came every 12 cycles once the sticks were in position, rather than 16. It handles one gold and one silver per loop, leading to an output every 3rd loop.
3rd place was SpiritualShampoo. His solution was very similar to mine, but explicitly makes the 255 atom brick and reshapes it in a long track station in the bottom. Mine managed to avoid such a large intermediate, but it was something I considered. Once it points left, the top 2 rows are the “copper upgraders” that function identically whether quicksilver or copper. The other 4 rows are the outputs-to-be. His solution had 150 instructions. In classic shampoo style, this was built without any quality of life mods, which he stated as the reason he wouldn’t consider doing any wand initialization.
My solution ended up scoring as 2nd place, at the time of the results stream. The only person who submitted something better was Kazyan.
Kazyan
First appearing in competition during the 2023 tournament, Kazyan quickly became a beloved community member. Known for both eloquent writing in the solution notes, and impressive performances on difficult puzzles, he delivered a 122 instruction masterpiece for Critellium RI. He went to the effort of initializing wands with a one-way track. The layout in general was more instruction efficient. It was a worthy winner.
Check out the “wandering hex-arm” tech that initializes the wands:
After thousands of cycles, the hex arm takes a place where it is useful in the steady state. This makes the effective cost of the setup only 1 instruction (track movement).
The other even longer track takes off on cycle 2327, carrying a wand of several copper and quicksilver to a station way in the top right. How far in the top right?
Unreasonably far.
His notes give a breakdown of how the instructions were spent:
One for initialization, via traveling hexarm. Fifty-five to extrude copper and quicksilver. Three to rectify polymer timing, moving waste elsewhere for further initialization. Two to bundle the polymers. Eight to purify to silver, six to project to silver. Four to reconnect and reshape. Eleven to gild. Two to transport. Thirty to disassemble into Critellium.
I could spend longer on this solution, given that it was a winner, but only two days after the results, a new submission appeared from someone who called themselves “0th place”.
Even Better
The winning solution was 122 instructions, but this 0th place solution was 93. Somehow it had slashed another 29 instructions with a fresh design. Not submitted during the tournament, it didn’t change any rankings. It also was a little more understandable than any of the winning solutions. Maybe only a little.
This 0th place submitter remained anonymous for a while. Immediately RP0 had asked “rebix is that you?” but rebix denied it. He had decided to stay out of the competition, having only submitted for a few weeks of the 2024 tournament anyway due to other priorities.
So who was this, and how would they describe their creation? A couple days later, we had our answer.
It’s the guy, from the sailcloth valley! Loving the absolute cursed energy that the RI competition produced, he had combined several ideas to build this more optimized solution. Below the 100 instruction barrier.
It stayed in the community eyes for a few more days, and Madmaster managed to make another improvement down to 91. But while celebrating the 2 instruction save, a new message by rebix spilled that it was going to be short lived.
It was still a counting solve. It was just the cleanest implementation of all.
The initialization hex arm creates a loop of iron, in addition to its work setting up wands.
The biggest instruction savings was in the process of making the copper and quicksilver bricks. After the 255 atom chunks came together, the remainder of the process resembles those that came before. The timing becomes pretty tight, but an arm that grabs and moves 3 times in its loop allows a whole 408 track segments of relatively fast movement. That’s the massive track on the right.
And so Critellium RI had its -1st place solution, beating the 0th place, and everything submitted by individual tournament competitors. It was half the instructions of the one I built. This was how most of the community viewed RI in the years since. Lower numbers than anyone could imagine, achieved incomprehensibly, by a few wizards.
Some philosophy
Are Opus Magnum solutions discovered or invented? Does a solution exist if nobody has made it? I think of these as mathematical objects, so my answer is the same as it is for mathematics. Yes the solution exists, and it is on us to find it. When given a complicated puzzle and an RI metric, the record is at best an approximation of the true peak of the solution space. What we do by creating our designs, is glimpse what may be out there. There are certainly personal touches to the individual solutions, which compound upon themselves when the people making solutions are inspired by what has already been discussed. But the true goal is perfection, which exists in a mathematical sense before and after we make our attempts.
When looking upon such complicated and borderline insane creations, I want to double down on this philosophy. We aren’t building these for sheer creative enjoyment. We build these because the metric calls them to our minds, and we cannot rest until the discovery is complete. If what we imagine is possible, it can be the new closest glimpse to the limit of the game. In this one niche direction combining two different measurements not provided by the game itself.
So now let’s fast forward to today.
2026 Tournament
Kazyan is hosting this year’s tournament right now. Week 5 just concluded, and rebix is the clear leader, by a margin that leaves him untouchable without disaster. The tournament also coincides with a huge surge of interest in Opus Magnum, combined from a viral video and a new DLC. As a result, there are over 200 people already in the rankings. The graph is more dense with names than any in previous years. See that green line on the far left, higher than every other by more than 10 points? That one is rebix. I’m the one next to him, in 2nd. Not bad.
Week 5 was an RI puzzle, and will be the subject of the rest of this blog post. It is called Tax Fraud.
You may recognize this as the inverse of Creative Accounting, a puzzle from the 2019 tournament where you do this process in reverse. Both puzzle names are fantastic, by the way.
Prior to the DLC, it was impossible to downgrade metals. Now there are glyphs of division and rejection, which each do just that. Gold into division produces two iron (not two silver, so as to avoid infinite loops with quicksilver). Rejection ‘traumatizes’ a quicksilver out of a metal, downgrading it one step in the process.
This isn’t just a fun gimmick using the DLC glyphs though, it is a seriously interesting puzzle with a lot of depth. In the newly accepted metallicity picture, the input has value 6, and the output value 10. This means that you can make 3 outputs from 5 inputs, leading to a similar situation to Refined Gold from much earlier. The ideal period is 10, and finding anything at a shorter period would be more complicated.
It’s no Critellium, but I think we don’t need another Critellium for quite a while. This is a good place to spend a week.
My thought process
Period 10 is too many instructions. I didn’t make one to confirm this, but I just knew it would be. Every duplicated grab-action-drop sequence I wrote on an arm would be emotionally painful. I could only handle period 4. At least so I thought.
After tinkering for a while, I realized the path I was following would lead to one of two problems. Option 1: I had to perform division on exactly 1/5 of the gold, an awkward ratio. Option 2: I had to implement a “Saverio’s transformer”, a construction introduced in the DLC where you combine purification and rejection to convert lead into quicksilver.
I do hold the current RI record for the Saverio’s transformer puzzle, but it is not instruction cheap.
And so I figured I needed to go with option 1. Counting to 5 became my headache.
With period 4, you pull atoms in two directions, meaning you don’t find your 5th in one direction until you have pulled 10 total. Then you have to do 2 divisions, and the timing between them has to be a multiple of 4, even though the machine period wants to be 20. Every counting problem gets moved to a new parity problem later. I had two different period 4 partial designs, but I didn’t finish either one.
Because I had a different crazy idea.
Period 5
Grabbing an input every 2 cycles is a key piece of rate optimization. Arms that repeat their instructions after an odd number of cycles, cannot do a grab on the input every single tape loop. They would cause a crash immediately by grabbing an input on the cycle it should be moving.
But it isn’t impossible to make a period 5 optimal rate solution.
Grimmy did it for Refined Gold years ago to prove a point:
In 5 cycles, an arm can grab, rotate, drop, and then rotate two more times to face the complete opposite direction. Any arm that grabs an input can do that, and it becomes responsible for one input per 10 cycles. It looks goofy as hell, but this solution achieves optimal rate (and even optimal cycles) at period 5.
An immediate consequence is that 5 separate arms need to grab the input. This is instruction heavy, at least 15 instructions if they are all tri-arms that don’t need the double rotation. But it solves the counting to 5 problem directly. One of your arms puts the gold in the division glyph. The other 4 do not. Done.
Tickled by this idea, I saw it through. And so my first RI solution to Tax Fraud was this 44 instruction period 5 machine:
There are no tracks, just a forest of multiarms. One pipeline (everything on the left) is responsible for turning 2 gold into one output and two excess quicksilver. The other pipeline is responsible for turning 3 gold into two outputs less two quicksilver. One bi-arm moves quicksilver from the left pipeline to the right to make the outputs. It’s the only arm with 5 instructions, while the rest have 3 and two no-ops.
I had no idea how good this solution actually was, and went back to period 4 optimization, expecting the limit of that would be something lower than 44. But the appeal of committing to period 5, the unreasonable odd period machine, was there. Tournaments are content farms and wacky decisions that turn out to be optimal are content.
Prior art
I had a look through the entire leaderboard, every currently tracked puzzle including DLC, journals, tournaments, lower stakes weekly competitions. Every one with an optimized RI solution chose an even period. Odd periods are not how you do rate. (Correction: Hangover cure has a period 3 RI solution! Thanks Grimmy!)
I justified my decision by pointing out that Tax Fraud is unique in that it has a single atom input and a lot of work you can do with it due to the DLC glyphs. The biggest showstopper for odd periods in the past is the input. 15 instructions is not nothing, but it is the value of a solution to the hardest problem in this puzzle.
I waffled in DMs with Kazyan between whether I should think harder about period 4 or optimize my period 5 to its limit. He said nothing, as tournament hosts are expected to do. They invite all DMs and take the role of a “rubber duck” who you are allowed to say anything to about their puzzle, during the time when all public discussion is prohibited.
In the end, I decided to stick with period 5, and optimized it down all the way to 36 instructions.
Each arm has at least 3 instructions. The biggest instruction savings come from doing work that was previously done by 2 arms, in only 1 arm. I cut the number of arms from 14 down to 11, and had only 3 extra instructions (the two arms on tracks) above every instruction tape being grab-action-drop.
I was confident this was either 1st or 2nd place. If I lost, I expected it would be to rebix.
Results
Streams this time around only cover the top 50 solutions. Those placed 51st or lower are covered in a separate stream by a different set of hosts. Kazyan opened this stream on 50th place, which was optimal rate in 97 instructions. Most submitters at these ranks were solving at period 10, some at period 4 such as Amaranth in 46th.
In 45th place we saw our first surprise. A player named rosa submitted a period 5 solution with 91 instructions. This alerted the chat to the possibility of period 5. Zannick and others began to conjecture it might be a great strategy.
It was period 10 vs period 4 for a long while after, without another appearance of period 5. The instruction counts also lingered in the 60s, making it into the 50s by the time we hit the top 10. Finally in 7th we saw the next period 5 machine by Jirekki, at 54 instructions. 6th place Shiinoe also made a period 5 machine at 54 instructions. It was starting to look better and better.
JonJon in 5th place made a very clean period 4 solution, hitting 50 instructions. It did have to solve the counting to 5 problem, but it shared quicksilver differently between the pipelines, allowing the excess to actually project iron up to silver, a strategy I had never considered. What I viewed as a parity problem became just the second pipeline all by itself, and saved a lot of headache.
Most surprisingly, 4th and 3rd place were period 10 solutions. Period 10 still went low enough to get onto the podium! For 3rd place, ebonnov had managed to build this period 10 solution with 47 instructions:
Then we got to the extremes. It was down to rebix and me.
Period 4
In 2nd place, with 43 instructions, was rebix’s period 4 machine. He titled it “can you hear the music?”
It has the one way track with the wandering hex arm, so let’s give it a chance from the beginning:
It’s amazing how the new DLC glyphs allow gold to create new atoms. The wandering hex arm doesn’t need many visits to the input to produce a huge number of wands. Also some creative spare atoms are used to help enter steady state in a different way. A lead is placed for the specific purpose of disposing a later unavoidable lead in a purification glyph. A wrong output is disassembled and the tin goes into a division glyph to get it out of the grippers of the hex arm carrying it.
The 20 cycle steady state loop looks like this:
I can see many incredible ideas here, all of them implemented as well as I can imagine period 4 doing them. On the left, a track loop counts to 5 by stealing 2 gold atoms out of 10 and feeding them one atom at a time into a big hex arm feeding division. Much like JonJon, rebix takes the approach of using projection to handle division output. The upper slappy stick is the main pipeline, while the lower one is the division outputs.
I can say that 43 is indeed lower than the 44 where I started, so I was right to be uncertain if I should be spending my time there. But it’s way higher than 36. I solidly won this metric, my only first place finish of this tournament so far.
Final Thoughts
After all the discoveries in RI from the past, it was still something new and unheard of, period 5, that was the insight for this puzzle. RI is just like that sometimes. Can’t discover what’s out there unless you get a little crazy.
Whether this puts us deeper into Sailcloth Valley or is the start of glimpsing enlightenment, is up to the reader to decide.