Opus Magnum — machine design guide: the numbers behind cost, cycles and area

Opus Magnum has no solution list worth publishing. Every puzzle accepts infinitely many machines, the game scores your machine on a histogram against everyone else's, and the whole point of the thing is that your answer is yours. What is worth publishing is the arithmetic: what each part costs, how far an arm actually reaches, what a cycle is worth, what each glyph does to an atom, and the input and output limits that decide how fast a design can possibly run. This guide is those invariants, so you can cost a machine on paper before you place a single part.

Written for the current Steam release: public branch build 24441428, updated 28 July 2026, plus the De Re Metallica expansion (released 17 March 2026; three new chapters, 17 new puzzles, three new glyphs and a "House Colvan" Sigmar's Garden variant). Nothing in this guide depends on the expansion. Every figure below comes from the game's own parts tray as recorded by the Opus Magnum wiki, or from the first-party/community engineering write-ups listed in Sources; where a number could not be confirmed it is flagged rather than filled in.

What the game scores, and when it stops

A level ends the moment you have produced 6 of each required output — six is the game's stand-in for "infinity" — and that moment is what every statistic is measured against.

Three things about the cycle counter that surprise people and that the optimisation scene treats as first principles:

• Cycle 1 is the first cycle on which any arm is programmed. All arms' tapes are padded with blanks to the same length, so every arm runs through exactly one machine period per loop. If nobody forces it, the period equals the longest arm's program.
• A clock instruction forces a longer period and is never counted as an instruction. Rate-optimal machines lean on this: a period-4 solution built from three-instruction arms uses one clock to hold the period at 4.
• Area is not "how big is my machine", it is "how many hexes were ever occupied", measured at the same instant as the cycles score. A cost optimiser can therefore run one arm through hundreds of instructions and still be small.

The wiki also publishes a compromise score for comparing all three at once: score = 300 / [(cost / best cost) + (cycle / best cycle) + (area / best area)], so 100% means a machine matched the theoretical best on cost, cycles and area simultaneously.

The rules that constrain every layout

These are the disposition and collision rules, straight from the wiki's Mechanisms and Commands pages.

• An arm's axle cannot share a tile with a reagent, a glyph, or another arm's axle — but arms pass over reagents and glyphs freely. New players burn time trying to keep the whole sweep clear; you only need the axle clear.
• One glyph per tile, and glyphs cannot overlap an arm's axle, a reagent or a track.
• A track may sit under an arm's axle, and any number of arms may share one track as long as they never collide. Track tiles connect to at most two neighbours, so tracks are linear or circular — no branches, no junctions.
• A collision is an arm's axle or a held atom occupying or passing through the same tile at the same time. The cost of a long arm is this: a 2- or 3-tile arm rotates through the tiles between start and end, and those passing tiles are live. Two atoms can never share a departure or an arrival tile, and a departure and an arrival cannot both lie on another atom's trajectory.
• Input limit: a reagent tile can be grabbed once every two cycles. This single rule decides the cycle score of most puzzles.
• Output limit: one product can be dropped per cycle. It is usually irrelevant, and the wiki calls it out as decisive in exactly two puzzles: Litharge Separation and Electrum Separation.
• One transformation per atom per cycle, except a multi-bond glyph, which can bond several directions at once. Bonding and calcification glyphs cost no instructions — which is why instruction optimisers move work into glyphs rather than arm movement.
• Reappearance: an element returns to its input tile at the end of a cycle only if all of the tiles it needs are free. Let something rest on the input and it starves. Rest a held structure there on purpose and you can suppress a respawn you do not want.

Mechanism prices and footprints

Straight from the wiki's mechanism table. Area is the hexes the mechanism itself occupies at minimum and maximum reach.

Notes that matter when you are spending money:

• Length is free, area is not. A 2- or 3-tile fixed arm costs the same 20 G as the 1-tile arm; it just claims more space.
• Multi-grip arms cost 30 G for two to six grips, and the wiki prices the triple and hex arms identically. More grips is the standard way to skip a reset instruction — a hex arm can pick up the next atom on the way round instead of rotating back to the start.
• A track under an arm is the cheap reach extender at 5 G a tile.
• The piston is the area play, not the cost play (18 reachable tiles for 40 G against 6 for a lone arm), and Van Berlo's Wheel is a fixed 30 G, 7 hexes, six arms' worth of grips that cannot extend.

Reaching tiles per gold, and per hex

The wiki publishes both sides of the reach trade-off, and they point in opposite directions. Cost first — reachable tiles for the money you actually spend:

And area — reachable tiles for the hexes you claim:

The wiki's own conclusion: for cost, a fixed arm with a 1-tile reach plus tracks where needed is the best option in most cases; for area, the piston arm is almost always more efficient. Note the shape of the answer — tracks buy reach at 5 G a tile up to 35 G, then the piston at 40 G leaps to 18 tiles and never looks back.

Glyph prices and footprints

The glyphs you will use most are also among the cheapest: calcification at 10 G is the answer to "I have the wrong element", and disposal is free but wants a hexagonal 7-hex footprint. A second 0 G glyph is listed with no effect at all, one hex.

Matching glyph shapes to mechanisms

Glyph shapes are not decoration — the shape tells you which tiles an arm must grip, drop or merely pass through, and therefore which mechanism set reaches it.

The costs here are the wiki's and they add up: 20 G arm, plus 5 G per track. The page's area column for this table does not reconcile with the mechanism table (it lists 1 hex for a set containing an arm that the mechanism table says takes 2 at minimum), so I have left it out rather than print a number I cannot stand behind.

The element graph in one page

Everything the transmutation engine can do to an atom, with the glyph and price:

• Cardinal to salt: Glyph of Calcification, 10 G. Salt back to a cardinal: Glyph of Duplication, 20 G. So any cardinal can become any other cardinal for 30 G of glyphs, and salt is the universal intermediate.
• Metal ladder: lead, tin, iron, copper, silver, gold. Projection (20 G) spends one quicksilver to move a metal one step up; Purification (20 G) fuses two atoms of the same metal into one of the next metal up. Projection costs quicksilver, purification costs an atom — the choice between them is the choice between feeding a second input and doubling your grabs.
• Vital elements: Glyph of Animismus (20 G) turns two salt into one vitae and one mors.
• Quintessence: Glyph of Unification (20 G) fuses the four cardinal elements into one quintessence; Glyph of Dispersion (20 G) takes it apart again. These appear in the journal chapters rather than the story.
• Bonds: every element takes at most six bonds. Simple bonds come from Bonding or Multi-bonding and are destroyed by Unbonding. Triplex bonds are fire-only, need all three bond lines passed, and Unbonding removes one even if only part of it formed. The wiki notes you can calcify and duplicate the atoms after bonding and carry a triple bond between non-fire elements — and that the game's own editors will not let you create that, so it is probably an unintended route.

The cycle arithmetic

The wiki's Theoretical Best page gives the formula the whole optimisation scene is built on:

cycles = (number of reagents grabbed per run - 1) x 2 + steps in the shortest transformation

The highest figure any input demands becomes the puzzle's cycle count. Three riders from the same page:

• If several input tiles feed the same reagent, the grabs are divided between them — this is the single biggest lever in the game.
• If two inputs share the highest count and their transformations must interact with a common third element, add a step (the wiki names Rocket Propellant, Stamina Potion, Warming Tonic, Life Sensing Potion, Stain Remover and Van Berlo's Wheel).
• Infinite products (the journal's chain outputs) subtract one step, because the product does not have to be dropped.

Here is the wiki's own cycle calculator for Refined Gold, the first puzzle of Act 1. It grabs 6 lead and 30 quicksilver per run:

The puzzle's cycle score is 62 — the quicksilver side, and 58 of those 62 cycles are nothing but waiting for the input to be ready. That is the shape of nearly every slow puzzle in the game. Rate-optimal play inverts it: the community's rule for a maximum-rate machine is to grab an input every two cycles, which requires at least two arms taking turns on each input tile, and Refined Gold's best rate is one output every 10 cycles. Face Powder reaches one output every 4 cycles by the same trick.

Useful comparisons from the same body of work: Airship Fuel wants 3 outputs every 8 cycles, and journal chain puzzles can have fractional rates (Sailcloth Thread's minimum is 3.6 rate — 10 monomers every 36 cycles).

Worked theoretical bests

The wiki builds a cheapest-possible machine for each product and prices it part by part. These are the totals, with the components it lists. Its own caveat: these optima ignore movement restrictions and may not be geometrically achievable.

Two lessons sit in that table. First, a single fixed arm plus one or two glyphs is the whole machine for most of the campaign — 40 G is a real target, not a theoretical stunt. Second, the expensive puzzles are expensive because of glyphs, not arms: Universal Solvent's cheapest build is 100 G of glyphs and a wheel plus one 40 G arm-and-tracks set.

Comparing the wiki's top-percentile figure with its theoretical best on the same puzzles shows where the community leaves room:

Cost converges first — the cheapest machine is usually found. Area and cycles are where the room is, and Timing Crystal (219 cycles, the slowest puzzle in the campaign) is the clearest example: the top percentile was 22 hexes away from the optimum.

The campaign, puzzle by puzzle

Reagents and the wiki's top-percentile benchmarks for every story puzzle, in order. Columns are cost, cycles, area.

Read the reagent column, not the puzzle names. Three Fire for Airship Fuel is a 19-cycle puzzle because the whole job is glyph work, while four Lead for Purified Gold is 112 cycles because it is five metal upgrades deep. The story also hands you the awkward shapes early on purpose: Refined Gold's 62 cycles is the first lesson in the two-cycle grab limit, one act before the puzzles that make you parallelise it.

The Appendix and the Journal

Appendix — 11 puzzles, tiny boards. Space is fixed by the level, so the appendix stops scoring area and scores instructions instead. The wiki's targets:

The Journal is the endless half of the game: 24 volumes published so far, twelve in Volume XCIX and twelve in Volume CVIII, each issue a themed batch of puzzles credited to a designer (some in-universe alchemists, some real community members who sent Zach Barth a puzzle). Each puzzle in it credits its author on the page. The most recent issue announced on Steam is Volume CVIII, Issue XII: Highlights from the Alchemical Exposition (16 June 2026), so the journal is still being added to. Journal material runs harder than the campaign, and it is where the chain outputs live — products that are infinite repeating polymers, scored by rate of monomer addition rather than drops.

The expansion adds its own three prequel chapters and 17 puzzles; the wiki's puzzle tables above do not include them, and neither does the wiki's glyph list (its three new glyphs, which the developer describes as manipulating metals, are not enumerated anywhere I could verify — community write-ups of DLC puzzles mention a division glyph).

Sigmar's Garden

The solitaire minigame is a hex board of 91 cells (side 6; the cell count is 3·6·5 + 1), holding marbles of 14 kinds, and you clear it by removing marbles in pairs. Free to remove means at least three contiguous empty neighbours, which is what makes the board a puzzle rather than a matching game.

Legal pairs, from the open-source clones and solvers rather than from the wiki's images:

• two marbles of the same cardinal element (air, earth, fire, water);
• salt with salt, or salt with a cardinal — salt is the wildcard, and it can also match another salt in the current rules (older builds did not allow salt-salt; a solver still ships an --old-rules switch for it);
• vitae with mors;
• quicksilver with a metal — and metals are locked in transmutation order: lead, then tin, iron, copper, silver, each paired with a quicksilver, then gold last on its own, with no pairing.

A standard board carries six metals (gold included) and five quicksilver. Solver invariants put at most eight marbles of any single cardinal on a board, and at most four vitae and four mors, always in equal numbers.

Strategy, borrowed from what the solvers do rather than from folklore:

• Getting the metals out is the whole game. A metal can only be taken once every lower metal is gone, so a quicksilver spent carelessly can strand the next metal with no legal partner. Take the current metal whenever it is playable and a quicksilver is free.
• Salt is how you fix parity. Elements with an odd count on the board can never pair off among themselves; each odd cardinal needs one salt, so count before you spend.
• Take the last of a kind when it is free — last vitae/mors pair, last quicksilver with the current metal, last salt with the last of an element. Those moves are safe; everything else is a search.
• The problem is genuinely hard in general: Sigmar's Garden is NP-complete, and the best solvers are exhaustive search with memoisation, or a SAT encoding. In practice a solver clears almost every board in well under a second, which is another way of saying the boards are friendly and the mistakes are yours.
• The expansion adds a House Colvan variant where metals are matched in sequential pairs (the developer's description), which removes much of the wildcard play above.
• The game keeps raising the bar on you as you win — one win, then ten, then twenty-five — so the metagame is volume, not a single perfect solve.

Traps that waste a first ten hours

1. "I need more arms" when you need more inputs. The two-cycle grab limit is the ceiling on every cycle score. One input tile per reagent means the fastest you can consume 30 atoms is 58 cycles no matter how beautiful the machine is.
2. Placing the arm's centre over the work. The axle cannot share a tile with a reagent, a glyph, or another axle. Arms may pass over anything, so the axle goes on empty ground adjacent to the work.
3. Building reach with arms when tracks are 5 G a tile. An arm plus three tracks reaches 10 tiles for 35 G; the piston reaches 18 tiles for 40 G. Almost everything in between is wasted money.
4. Ignoring the swept tiles of a 2- or 3-tile arm. They are real collision volume, and two atoms cannot share a departure or an arrival, nor have both their departure and arrival on another atom's path.
5. Letting your own machine starve its inputs. An element only respawns if all of its tiles are free. Atoms parked on the input are the classic silent slowdown — and deliberately parking a held structure there is a legitimate technique for suppressing respawn you do not want.
6. Assuming one product per cycle is fine. It is, except in Litharge Separation and Electrum Separation, where the wiki calls it out as the binding constraint.
7. Spending quicksilver when purification is cheaper — or the reverse. Projection eats a quicksilver per upgrade; purification eats a second atom of the same metal. On a puzzle with no quicksilver input, purification is the only ladder.
8. Placing an arm's axle over a Van Berlo's Wheel's held elements. The editor accepts it; the simulation collides immediately. The wheel is 7 hexes of occupied ground and it cannot extend.
9. Triple bonds look like ordinary bonds. Only fire elements can make them, all three bond lines must be passed to complete one, and Unbonding will happily remove a triplex bond even if only one of the three parts was formed.
10. Believing a wiki number because it is in a table. While writing this I found: three anchor ids on the Mechanisms page sitting one row off their rows (the piston, track and wheel anchors are all misplaced); the Bonding and Multi-bonding rows on the Glyphs page carrying identical descriptions; a glyph-shape table whose area column contradicts the mechanism table; and product pages with theoretical-best rows that are plainly mistyped (Conductive Enamel's cost is listed as 880 G, several puzzles have no area figure at all). Where the machine table and the cost breakdown disagreed, I used the machine table.
11. Not knowing when your score stops counting. It stops at the 6th product. Everything after that cycle is free, which is exactly what cost and area optimisers exploit with one-arm, hundred-instruction machines.
12. Optimising all three at once on your first pass. Build it ugly, win, then pick one number and rebuild for it. The compromise formula rewards a machine that is merely good at all three, and the histograms reward a machine that is best at one.

Sources

All wiki content was read as raw wikitext through the MediaWiki API (api.php?action=parse&prop=wikitext), because rendered wiki pages show ingredient icons instead of the quantities.

• Opus Magnum wiki (opus-magnum.fandom.com): Products, Mechanisms, Glyphs, Elements, Commands, Theoretical Best, Appendix, Journal, Sigmar's Garden, plus the per-product pages used for the cost breakdowns: Refined Gold, Face Powder, Airship Fuel, Explosive Phial, Mist of Incapacitation, Purified Gold, Alcohol Separation, Universal Solvent, Timing Crystal.
• Korean-language reference (namu.wiki content mirrored at seore.org) for the multi-bonding glyph acting in three directions at once, the Appendix being scored on instruction count, and the Van Berlo's Wheel axle-overlap trap.
• Biggieblog: "Defeating Refined Bronze (and losing a cow bet)" — the score definitions, the 6-products-is-infinity win condition, tapes padded to one machine period, area measured at the win cycle, and the journal's credited-designer structure.
• Biggieblog: "Combining Rate and Instructions to Create Beautiful Madness" — the two-cycle grab requirement and two-arms-per-input rule for rate-optimal machines, the free clock instruction, Refined Gold's 10-cycle rate and Airship Fuel's 3-outputs-per-8-cycles rate, Sailcloth Thread's 3.6 rate, and the DLC's metal-manipulating glyphs including a division glyph.
• Max Ruigrok, "Generating and Solving Sigmar's Garden Puzzles" (LIACS bachelor thesis, 17 July 2025) — NP-completeness proof, the 91-cell board of side 6, six metals including a keyless gold, and five quicksilver.
• Solver projects, used for the marble pairing rules and board invariants: mvidell.se's Sigmar's Garden solver (91 marbles, free means three or more empty neighbours, the old salt-cannot-match-salt rule), marvk/sigmarsgarden (full legal-move generation: two elements, two salts, salt plus element, mors plus vitae, quicksilver plus any metal, and metals blocked by earlier metals), dewiniaid/sigsolve (at most eight marbles per cardinal, at most four vitae and four mors, always equal), cursande/claudion (the marble families and the metal removal order).
• Steam, for the game's current state: store API for app 558990 and for the De Re Metallica DLC, app 3107410 (released 17 March 2026; 17 puzzles, three new glyphs, House Colvan variant), the news feed for app 558990 (latest journal issue Volume CVIII Issue XII, 16 June 2026; latest update 28 July 2026), and public buildid 24441428 from the Steam app-info API.
• Wikipedia: Opus Magnum and the developer's De Re Metallica page for the expansion's announcement (19 February 2026) and release.

Written for: Opus Magnum public branch build 24441428 (updated 28 July 2026); base game plus De Re Metallica (17 March 2026).

Unverified, and left out rather than guessed: the names and exact effects of De Re Metallica's three new glyphs (the wiki's glyph table has not been updated for them, and the developer's page only says they manipulate metals); the wiki's definition of "top percentile" (the term is used throughout its tables but never defined on the pages I read, so treat those columns as published benchmarks rather than a documented in-game statistic); whether the 2026 Volume CVIII journal issues require the expansion or shipped with the base game; and the fine print of within-cycle execution order — a community reverse-engineering document describes glyph updates and collision checks happening twice per cycle, which does not sit comfortably with the two-cycle input figure the wiki's cycle maths is built on, so I used the wiki's figure and left that point alone.