A Beauty Cold and Austere

**A Beauty Cold and Austere** is a Glulx interactive fiction game written with Inform 7 and is © 2017 by Mike Spivey. It was an entry in IF Comp 2017 where it took 7th place.

In this puzzle-filled game, you play as a college or university student who skipped most of their classes in conceptual mathematics. Your final exam is tomorrow! But it's late and you're tired and cramming never worked for you, so... you're going to eat one of your roommate's weird blorple pills and explore your math book's mystic energy field in your dreams.

This solution is by David Welbourn, and is based on Release 1 of the game.

- Maps
- Tutorial Walkthrough
- Walkthrough
- Extras
- Thank You to my Patreon supporters
- External links:

Note that the location names on the number line change as new locations are found.

- Point ⇒ Positive Axis: 1 ⇒ Number Line: 1 ⇒ Real Axis: 1
- Positive Axis: 2 ⇒ Number Line: 2 ⇒ Real Axis: 2
- Beginning of Positive Axis: 0 ⇒ Number Line: 0 ⇒ Origin
- Number Line: −1 ⇒ Real Axis: −1

Likewise, the locations below "One" alter:

- Void ⇒ Form ⇒ Matter ⇒ Gray Matter ⇒ Gray Matter, Level One
- Darkness ⇒ Twilight ⇒ Gray ⇒ Gray Matter, Level Two
- Confusion ⇒ Less Confusion ⇒ Gray Matter, Level Three
- Blinding Light ⇒ Light ⇒ Gray Matter, Level Four

Note: When the poker game is over, "Poker Game" is renamed to "No Longer a Poker Game".

Note: The directions shown in the Intersection locations are just a suggested traversal of the space. Connections between intersections are not one-way.

`> x book. look.`

College Library

`> look up newton.`

`> green her. tell librarian about final.`

`> get book and cup. i. give cup to librarian.`

`> s.`

Your Dorm Room

`> x desk. read note. x bottle. read it.`

`> i. x book. x bed. look under bed.`

`> x posters. x movie. x game. x vegas. x park.`

`> listen. open bottle. eat pill.`

Note: You can only sleep carrying one item. Make sure that item is the book.

`> lie down. sleep.`

Point

`> x disk. x hole. x space.`

`> look up point. look up arithmetic.`

`> d.`

One

`> d.`

Void

`> take wand. x it. u.`

One

`> wave wand.`

Two

`> u.`

Positive Axis: 2

The wand at One to the west stretches itslef into a number, running west to east, with you at "2".

`> look up number line.`

`> w.`

Positive Axis: 1 *(formerly Point)*

There's nothing west of here, but we can still go down.

`> d. d.`

Form *(formerly Void)*

`> w.`

Great Hall

`> x puppet. look up counting.`

`> greet Count. x coins. count coins.`

`> ask Count about puppet. ask Count about Sesame Street.`

`> ask Count about Big Bird.`

`> w.`

Castle Chapel

`> x icons. x triangle. look up pascal's triangle.`

So, the Count's number would be C(10,5). Since we only have rows 0 to 8 of the triangle available, use C(n,k) = C(n−1,k) + C(n−1,k−1) to break it down.

C(10,5) = C(9,5) + C(9,4) = C(8,5) + C(8,4) + C(8,4) + C(8,3) = 56 + 70 + 70 + 56 = 252.

`> e.`

Great Hall

`> tell count about 252.`

`> x coin. s.`

Solar

`> x tapestry. x table. x calculator. x puppet.`

`> greet puppet.`

`> ask her about box. ask her about tapestry.`

`> ask her about multiplication.`

`> ask her about count. ask her about castle.`

`> ask her about icons. ask her about herself.`

`> x box. x knobs. x wheels.`

`> n. e. e.`

Scholar's Study

`> x designs. x note. x root.`

`> take root. look up root.`

`> x coffer. open it.`

`> s.`

Alcove

The scales represent three equations. Solve for x, y, and z by removing blocks and pebbles from both pans of a scale simultaneously — remember, how in the tutorial you could take book __and__ cup? — while keeping the scales balanced.

`> x scales.`

First, solve the bronze scale: 2x + 2 = 12.

`> take two tan and two sepia.`

`> take one brown x and five sepia.`

Second, solve the silver scale: 3y + 6 = x + 10.

`> take gray x and five ash.`

`> take ash and one slate.`

`> take two gray y and six slate.`

Third, solve the gold scale: x + z + 4 = y + 8.

`> take yellow x and five maize.`

`> take yellow y and three sand.`

`> take one sand and one maize.`

A tiny key is your reward.

`> take key. n.`

Scholar's Study

`> unlock coffer with key. drop key. open coffer.`

`> x ring. take it.`

`> w. u.`

One

`> wear ring.`

Zero

This set object is a hold-all; we won't have to worry about inventory limits while we have this.

`> take set. x set. x nothing.`

`> u.`

Beginning of Positive Axis: 0

`> e. d. d.`

Form

`> s.`

Librarian's Office

`> x scrolls. x numbers. look up primes.`

`> push 1.`

`> push switch.`

`> push 2. push 3. push 5. push 7.`

`> look up number theory.`

`> s.`

Map Room

`> x maps. x globe. x pedestal. x gap.`

`> turn globe. x lines. x longitude. x latitude.`

`> look up geometry.`

`> n. n. n. `

Lyceum

`> x stadium. x temple. x home. x road.`

`> ne. ne.`

Dead End

It's unclear to me what precisely triggers the changes in the Gray Matter locations in this game, beyond gaining points. Possibly visiting new locations, even useless ones like this one, might help your progress. I'm not sure, so I'm including it.

`> sw. n.`

Hilltop

`> x Euclid. greet Euclid. x scroll. read it.`

`> look up Euclid. look up postulates.`

`> tell him about globe. tell him about lines.`

`> tell him about longitude.`

`> x elements. s. sw.`

Lyceum

`> e.`

Courtyard

`> x pedestals. look up Plato. d.`

Cave

This appears to be Plato's Cave.

`> x shadows. x chains. u. w. w.`

Stadium

`> x Achilles. greet him. look up Zeno. look up limit.`

`> ask him about Zeno. ask him about tortoise.`

`> tell him about limit.`

`> e. n.`

Temple of Number, Southern End

`> x columns. x inscription. n.`

Temple of Number, Northern End

The acolyte won't let you go north.

`> x acolyte. greet her. x urn.`

`> take scrap. read scrap.`

The scrap claims that only odds, evens, and ratios can exist.

`> x statue. look up Pythagoras.`

`> s. s. s.`

Matter *(formerly "Form")*

`> x inscription. u. u. e. d.`

Two

Using the square root:

`> extract.`

Irrational: Between 1 and 2

`> take proof. x it.`

`> u.`

Positive Axis: 1

`> d. d. n. n. n.`

Temple of Number, Northern End

`> drop scrap.`

`> drop proof.`

`> n.`

Inner Sanctum

You can abbreviate the names of solids by dropping the -hedron part.

`> x octa. x staff. x sandals.`

`> take all.`

`> look up Archimedes. look up Eudoxus. look up exhaustion.`

`> s. s. s. e.`

Courtyard

`> put octa on medium triangle.`

`> w. w.`

Stadium

Although the sandals help, they're not quite good enough.

`> give sandals to Achilles.`

`> wear sandals. race him.`

`> e. s. s. s.`

Map Room

`> put staff in gap. move globe.`

`> x pedestal. x tetra. take tetra.`

`> n. n. n. e.`

Courtyard

`> put tetra on large triangle.`

`> w. s. e.`

Scholar's Study

With better Geometry, the designs make more sense to you.

`> x designs. x buttons. x note.`

Type out "3.1415" via the buttons, where the numerical value of the button is the number of sides it has:

`> push triangle. push circle. push square.`

`> push circle. push pentagon.`

`> e.`

Hidden Room

`> x cube. take it.`

`> x chest.`

I confess I solved this the hard way, but if you remember the entry for Pascal's Triangle, it offers a shortcut:

`> look up pascal's triangle.`

`> set first to 1. set second to 4. set third to 6.`

`> set fourth to 4. set fifth to 1.`

`> look up algebra.`

`> open chest. x compendious. take it.`

`> w. w. n. e.`

Courtyard

`> put cube on square.`

`> w. s. d.`

Darkness

`> take mirror. x mirror.`

`> u. u.`

One

`> look in mirror.`

Negative One

`> x inverter. put coin in inverter.`

`> u.`

Number Line: −1

Although the line continues west, there's nothing notable near here that way.

`> e. e. d. d. d.`

Twilight *(formerly "Darkness")*

`> n.`

Grassy Area

`> x homework. look up logarithms.`

`> x slide rule. take it.`

`> x ball. take it. kick it. look.`

`> x ico. take it.`

`> x table. x grass. x gate.`

`> e.`

Laundry Room

I have no idea why this room is in the game.

`> x sign. x washing. x dryer.`

`> turn on washing. turn on dryer.`

`> w. s.`

Gray *(formerly "Twilight")*

`> x inscription. x bin. x ghost. greet ghost.`

The ghost will tell you if something you have is still useful.

`> show scroll to ghost.`

`> w.`

Casino

`> x machine. push white button.`

Unfortunately, this minigame is randomized, so you may have to play the machine's game a few times before you win it.

Blue rejects all numbers until it gets a higher number than the one you just had.

`> push black.`

`> push blue.`

`> push green.`

If you didn't win, return to push black and try again until you do win.

`> look up optimal stopping problem.`

`> n.`

Poker Game / No Longer a Poker Game

`> x game. x Pascal. look up Pascal.`

`> x paper. take paper. x paper. put paper in pocket.`

`> x Bayes. look up Bayes. look up probability.`

`> x Kolmogorov. look up Kolmogorov. x Diaconis. look up Diaconis.`

`> greet Pascal.`

You won't be able to win until you've won the game in the Casino first.

`> put coin on table.`

`> look. x pile.`

You don't need the pile of money, the paper, or the coin any more. Leave 'em.

`> s.`

`> x dodeca. take it.`

`> s. e. e.`

West of House

`> x house. x door. x mailbox. x hole. open mailbox.`

`> x boards. take boards. open door. e.`

Living Room

`> x sofa. x bookcase.`

`> put elements in case.`

`> put algebra in case.`

`> w. w. s.`

Physician's Office

`> x parchment. x piece of metal.`

`> put metal on parchment.`

`> xyzzy. x ars magna. take it.`

`> x instruments. look up cardano.`

`> x mechanism. x crank. x gears. x bar. x panel.`

`> open panel. x wave.`

`> turn crank. take wave. turn crank.`

`> n. u. u. u. w. w. d.`

Negative One

`> put sine in inverter.`

`> x negative sine.`

`> extract.`

`> u. e. e. d. d. w. s.`

Solar

Note: You must first have looked up logarithms in your math book or the Countess won't accept the slide rule.

`> show slide rule to countess.`

`> x arithmetica. x margins.`

`> look up Diophantus. look up Fermat. look up Descartes.`

`> n. e. n. e.`

Courtyard

`> put ico on small triangle.`

`> put dodeca on pentagon.`

`> x sphere. take it.`

`> w. s. d. e. e.`

Living Room

`> put ars in case.`

`> put arithmetica in case.`

`> w. w. s.`

Physician's Office

`> put negative wave in panel. turn crank.`

Your square root is imbued with negative energy.

`> n. u. u. u. w. w. d.`

Negative Ove

Using the square root imbued with negative energy:

`> extract.`

Imaginary Unit

`> u.`

Imaginary Axis: i

`> s.`

Origin *(formerly "Number Line: 0")*

The number line is now the real axis.

`> e. d. d. d. d.`

Confusion

`> x fog. u. d.`

Less Confusion *(formerly Confusion)*

`> n.`

Barn

`> smell. x farmer. x wood. greet farmer.`

`> x card. ask farmer about problem.`

A cowbell interrupts. Farmer goes to see to Bessie, but leaves Pennings, a dog, who will carry your solution to the farmer.

`> x dog. look up pennings.`

`> pet dog. dog, beg. dog, play dead. dog, roll over.`

`> s. e.`

Neon-Lit Room

`> x lights. x bike. x comic.`

`> ride bike.`

Intersection *(several locations)*

You need to illuminate all the grid lines. One ramp jump is allowed.

`> ne. e. s. s. w. w. n.`

`> se. n. e. nw. s. w.`

Neon-Lit Room

`> stand. x analysis. take it.`

`> look up Euler. look up Gauss.`

`> w.`

Gray Matter, Level Three *(formerly Less Confusion)*

`> x inscription. w.`

Great Court

`> x fountain. w.`

College Hall

`> look. x notes. take notes. look up Berkeley.`

`> x podium. x paneling. e. n.`

College Chapel

`> x statue. greet Newton. x circle.`

`> put sphere in circle.`

Giant's Shoulder

`> x Newton. look up Newton.`

`> x valley. x lake. x forest. x mountain.`

`> greet Newton.`

`> answer derivative.`

`> answer slope.`

`> answer zero.`

`> answer mountain.`

`> x range.`

`> show notes to Newton. look up Cauchy.`

`> jump. s. e.`

Grey Matter, Level Three

The fog is all gone, revealing a way down.

`> d.`

Blinding Light

Nothing to do here yet.

`> u. s.`

Roller Coaster Entrance

`> read brochure. look up Descartes.`

`> x river. x coaster. x notice. u.`

Boarding Platform

`> x car. x loop. enter car.`

`> d. e.`

Operator's Office

`> x display.`

`> x slot. x saying. x correspondence. look up folium.`

`> x finder. x carabiner.`

`> take finder. take saying. take correspondence.`

`> put card in slot.`

`> w. u.`

Boarding Platform

`> derive.`

`> x finder. remove film. x wad. drop wad.`

`> attach finder to loop.`

`> enter car. x finder.`

`> take finder.`

`> d. n. n.`

Barn

`> give finder to dog.`

`> drop finder.`

`> s. d.`

Light

`> n. `

Smoky Pub

`> x Cauchy. x Weierstrass. look up Weierstrass.`

`> x wine. x beer.`

`> greet Cauchy. look up complex analysis.`

`> look up complex. look up imaginary.`

`> look up complex plane. look up real number. look up infinity.`

`> show notes to Weierstrass. x wine. x beer.`

`> give sandals to Weierstrass.`

`> x shoes.`

You need to have points in Complex Numbers for this to work:

`> give root to Cauchy.`

`> s. u. u. u. u. u. w. n. d.`

Imaginary Unit

Using the augmented square root:

`> extract.`

Complex: Modulus 1 and Acute Angle

Good grief. This is one of the most awesome and frightening location names that I've ever seen in interactive fiction.

`> x foundations. take it. look up Riemann.`

`> u.`

Real Axis: 1

`> x plane. x stars. count stars.`

`> d. d. d. e. e.`

Living Room

`> put foundations in case.`

`> put analysis in case.`

`> w. w. u. n. w.`

Stadium

`> give shoes to Achilles.`

`> look. take scroll. read it.`

`> e. s. d. d. d. w.`

Research Lab

The sliders can be set to −1, 0, or 1, and only change the top row of the matrix.

`> x door. x platform. x panel. x sliders. x first slider.`

`> x fan. read printout.`

`> turn on fan.`

`> turn off fan.`

`> n.`

Seminar Room

`> x slides. x window. x courtyard.`

`> x first page. x second. x third.`

`> x fourth. x fifth. x sixth. x seventh.`

`> look up matrix. look up transformation.`

`> s. s.`

Graduate Student Office

`> x desks. x window. x building.`

`> n.`

Research Lab

Okay, let's make ourselves two-dimensional, briefly. You want the top line of the display to be all zeroes; this isn't the only combo that works:

`> set second slider to 0.`

`> turn on fan. stand on platform. push button.`

The fan blows your 2D self under the door to...

Professor's Office

`> x finite. take it. look up Halmos.`

`> x desk. open drawer. take spare key.`

`> x window. x campus.`

`> e.`

Research Lab

`> turn off fan. drop key. e. e.`

Machine Room

I don't really understand what's happening here. I think one set of numbers on the path steps are numerators and the other set are denominators, so each step represents a ratio that you're adding as you go forward? And if you're wearing the limit shoes, the sum of your path will take you to some number ... or to Infinity. Unless the warning light is on, in which case you risk waking up prematurely.

`> x machine. x path.`

Fortunately, it's easy enough to lawnmow through combinations of settings until you get something you like. Try Identity Series first:

`> set dial to identity. set switch to series.`

`> s. wear shoes. s.`

Infinity

`> x Ramanujan. greet him. look up Ramanujan.`

`> x booth. x nothingness. take it.`

`> look. take integer. x integer.`

`> enter booth. push crystal button.`

Grand Hotel

`> x clerk. greet clerk.`

`> d.`

Infinity

`> talk to Ramanujan.`

`> enter booth. push clear button.`

Zero

`> u. e. d. d. d. d. d. e.`

Machine Room

Try "Reciprocal Series" next. The switch is already at Series.

`> set dial to reciprocal. x path. s.`

Infinity

`> enter booth. push crystal.`

Grand Hotel

`> tell clerk about double.`

`> w.`

Grand Court

`> take rod. x it.`

`> x trees. e. d.`

Infinity

`> show rod to Ramanujan. enter booth. push clear.`

Zero

`> u. e. d. d. d. d. d. e.`

Machine Room

Finally, put the rod in the hole and set the controls to Alternate Reciprocal Series. Make sure you have the square root!

`> put rod in hole.`

`> push alternate. x path. s.`

This is really really weird, but by changing the order that this series is added, you can get any total value you like, and in this case, we (and the rod) like 69,105. So that's where we end up.

69,105

`> x leaves. count leaves. take leaves.`

`> u.`

Real Axis: 69,105

`> w. e. d.`

69,105

If you don't have the square root with you, you might be stuck here, with no option but deliberately waking yourself up.

`> extract.`

Irrational: Between 1 and 2

`> u. d. d. w.`

Great Hall

`> give leaves to count.`

`> i. x liber. look up Fibonacci.`

`> e. d. d. w. n.`

College Chapel

`> put sphere in light.`

Giant's Shoulder

`> give range to Newton. x principia.`

`> jump. s. e. d.`

Gray Matter, Level Four

At 82 points or so, the patch of light becomes a book.

`> x inscription. x disquisitiones. take it.`

`> s.`

Window into Oblivion

Descartes can't think where he is.

`> x window. x pile. x Rene. x tray. greet Rene.`

`> show saying to Rene.`

`> put saying in tray. take saying.`

`> put largest integer in tray.`

`> greet Hypatia. x her. look up Hypatia.`

`> ask her about Descartes. ask her about imps.`

`> show correspondence to her.`

`> show saying to her.`

`> show logic scroll to her.`

`> i. x crank. n. w.`

Research Lab

Make sure the top row of the panel is 0 1 0.

`> set second slider to 1.`

`> put crank on platform. push button.`

`> take crank. e. u. s.`

Roller Coaster Entrance

`> x notice. e.`

Operator's Office

`> take la. x la.`

`> w. n. u. e.`

West of House

The crank must be inverted before it will fit.

`> put crank in hole. turn crank.`

`> take package. x it. open it.`

`> x art. look up Knuth. x brown paper.`

`> e.`

Living Room

`> put finite in case.`

`> put liber in case.`

`> put principia in case.`

`> put disquisitiones in case.`

`> put la in case.`

`> put art in case.`

`> x case.`

`> take fractals. x it. read it.`

`> look up fractals. look up Mandelbrot.`

`> w. w.`

Gray Matter, Level Two

Last chance to futz around.

`> show fractals to ghost.`

`> show brown paper to ghost.`

`> put set in set. look up Zermelo.`

`> look up topology.`

`> u. u. u.`

Real Axis: 1

`> read fractals.`

`*** With a score of 100 on the exam you earned an A+ in the course. ***`

`> amusing`

`> credits`

`> math`

>amusingHave you tried...

- Examining the posters in your dorm room?
- Looking under your bed?
- Going to sleep in your bed while carrying something other than the math book? While not carrying anything?
- Waking up while dreaming? While awake?
- Giving the exhaustion sandals to Achilles?
- Open or closing the set with or without something in it?
- Putting the set into itself when it is empty? When it has something in it?
- Asking the Count or Countess about PUPPET?
- Interacting with "nothing" in Zero?
- Looking in the mirror while in Zero, Two, or Irrational Between 1 and 2?
- Breaking the mirror?
- Turning the crank on the strange mechanism when the sine wave or cosine wave is not in it?
- Looking up Pennings in your math book?
- Giving Pennings standard dog commands, such as PENNINGS, FETCH?
- Throwing an object while Pennings is present?
- Giving Berkeley's lecture notes to Newton?
- Casting EXTRACT in Infinity?
- Repeatedly examining the pile of discarded objects in Oblivion?
- Examining the glass of wine and the mug of beer before and after helping Weierstrass?
- Listening to all of Hypatia's phone calls?
- Reading the new notice at the roller coaster after rescuing Descartes?
- Attacking something? Throwing something?
- Thinking in your dorm room? Thinking during the dream?
- Singing repeatedly?
- Praying?
- Fixing yourself? Another person?
- Eating a book? Yourself? Another person? The old coin?

I'll add a few other things:

- I was amused that the windows in the Seminar Room and Graduate Student Office open, but the bay window in the Professor's Office does not, coupled with the observation that the professor's view is great, but the view that the students get is poor.
- The Laundry Room seems entirely unnecessary, but you can still try turning on the washing machine and dryer.
- Try counting various things, like the leaves, the stars, the pile of money.
- Race Achilles with or without the exhaustion sandals or limit shoes.
- The Cave below the Courtyard is a reference to Plato's Cave, of course.
- You can enter the fountain at Great Court.

Characters you can interact with:

- A
**librarian**is in the college library in the tutorial part of the game. - The
**Count**, a purple puppet, is counting coins in his Great Hall. - The
**Countess**, another purple puppet, is trying to fix a machine in her Solar. - An
**acolyte**is sweeping the floor in the Temple of Number. **Achilles**is moping in the Stadium because he can't beat a tortoise in a footrace.**Euclid**ponders postulates on a Hilltop.- The
**gray lady**is a ghost who appears in Gray Matter, Level Two. She'll help you assess which of your inventory items are still useful to you. - A
**farmer**is trying to make a barrel in his Barn. **Pennings**is the farmer's dog. He's in the Barn when the farmer is not.**Sir Isaac Newton**will talk to you on top of a Giant's Shoulder.**Pascal**,**Kolmogorov**,**Diaconis**, and**Bayes**are playing poker.**Cauchy**and**Weierstrass**are drinking in the Smoky Pub.**René Descartes**is floating in oblivion, unable to think.**Srinivasa Ramanujan**is chilling at Infinity.**Hypatia**is a woman in charge of Oblivion.

Characters seen briefly:

- A
**servant**of the Count and Countess brings things to them. - A
**tortoise**races Achilles in the Stadium whenever Achilles gives it a try. **Zeno**chats and walks off with Achilles after Achilles wins his race.- A
**bartender**appears in the Smoky Pub to whisk away used glassware. - An
**imp**appears when Hypatia calls for it to rescue René. - New
**guests**of the Grand Hotel rush through its lobby once the clerk knows where to put them. - Your
**math professor**administers and comments on your test results in the epilogue.

Characters only heard:

- Your fellow
**students**are partying outside your dorm room. **Bessie**, the farmer's cow, rings her cowbell.- A
**voice**, sounding like your math professor, tells you something about each mathematics text when you put it into the Living Room's bookcase. - Other
**people**are playing games in the Casino.

Also:

**Pythagoras**has a statue in the Temple of Number.- Many
**people**talk to Hypatia via her cellphone.

>credits

Cover art: Cody J. Lail Design | www.codyjlail.com

Testing: Sam Burdick, Daniel Hyams, Alex Kaufman, Keetie, Todd Rorem, Brian Rushton, Andrew Schultz, Daniel Spivey, Daniel Stelzer, David White, jkj yuio

Technical assistance: Andrew Schultz

Inform 7: Graham Nelson

Extensions to Inform 7: Eric Eve, Jon Ingold, Jesse McGrew, Graham Nelson, Emily Short

General advice and encouragement: Brian Rushton

Mathematics sources: A History of Mathematics, by Victor J. Katz, was indispensible, as was Wikipedia. (Wikipedia has a bad reputation for reliability, but I have found its mathematics pages to be quite good. Information about historical figures obtained from Wikipedia was generally double-checked against other resources.)For further reading on the history of mathematics I recommend Men of Mathematics, by Eric Temple Bell. It's a bit old (1930s), but it's still the most lively and readable book on mathematicians and the history of mathematics that I know.

Interactive fiction inspirations: Infocom, of course. A Beauty Cold and Austere contains references to or riffs on puzzles from several Infocom games: Zork 1, Zork 2, Enchanter, Sorcerer, Spellbreaker, Hitchhiker's Guide to the Galaxy, A Mind Forever Voyaging, and Trinity.Trinity, by Brian Moriarty, deserves special mention. The structure of Trinity is somewhat repeated in ABCA, and the Klein bottle puzzle in Trinity was an inspiration for the idea of introducing advanced mathematical concepts through the medium of interactive fiction. (Playing Trinity at age 13 was my introduction to a Klein bottle.) The crank puzzle in ABCA is of course a riff on the Klein bottle puzzle in Trinity.

Curses!, by Graham Nelson. After the demise of Infocom in the late 1980s, I mostly gave up playing interactive fiction for the better part of 30 years. In February of 2017 I decided to try Curses!. It inspired me both to take a serious look at "modern" interactive fiction and to write a piece of IF on my own.

GiantKiller, by Peter D. Killworth, and The Chinese Room, by Harry Giles and Joey Jones. When I was trying to decide what level to aim for with ABCA, these two games convinced me to go high.

Quotations: "Euclid alone has looked on Beauty bare" is by Edna St. Vincent Millay.

The quote likening mathematics to a blind man in a dark room has been attributed to Darwin, but it's questionable whether he actually said that.

The poem about infinite series is by, believe it or not, a mathematician: Jakob Bernoulli.

"Tell all the truth but tell it slant" is by Emily Dickinson.

The poem in Italian you hear after creating the fractal consists of selections from Dante's Paradiso, Canto XXXIII, as Dante is approaching his final vision of God.

You have an inventory limit of six items, until you get the set, which acts like a rucksack and can hold any or all of your inventory items (except itself).

Tutorial inventory:

- your
**math book**. It's on the table. Look up Newton and take the book when prompted to do so. Since this is the same math book as in the main game, you can look up any valid topic instead of Newton. - an
**empty yogurt cup**. It's on the table. Take it and give it to the librarian when prompted to do so.

Books:

- your
**math book**. You're carrying it and don't lose it. It's the most important item in the game. - In Your Dorm Room, after you eat the pill, drop all your other possessions (eg: bottle, note) and get in bed with the book. Then
`sleep`to enter a mathematical dream world. `Look up`topics in your math book, usually either mathematical concepts or people's names.- In particular, you must look up logarithms (or slide rule) to learn how to use the slide rule before you can give it to the Countess.
- Known topics include: Al-Khwarizmi, algebra, Archimedes, arithmetic, Bayes, Berkeley, calculus, Cantor, Cardano, Cauchy, complex analysis, complex number, complex plane, counting, cube, derivatives, Descartes, Diaconis, Diophantus, dodecahedron, Elements, Euclid, Eudoxus, Euler, exhaustion, Fermat, Fibonacci, folium, fractals, Gauss, geometry, Halmos, Hypatia, icosahedron, imaginary number, infinity, integral, integration, Knuth, Kolmogorov, Leibniz, limit, logarithms, Mandelbrot, math, matrix, Newton, number line, number theory, octahedron, optimal stopping problem, Pascal, Pascal's Triangle, Pennings, pentagon, Plato, Platonic solid, point, polygon, postulates, primes, probability, Pythagoras, Ramanujan, real number, Riemann, set theory, sine, square, square root, tetrahedron, topology, transformation, triangle, Weierstrass, and Zeno.
**Elements**. At Hilltop, Euclid will give this book to you after you tell him about longitude; you probably need to examine the globe in the Map Room first. Put the book in the Living Room's bookcase.**Introduction to the Analysis of the Infinite**. It's in the Neon-Lit Room after you successfully solve the bike puzzle. Put the book in the Living Room's bookcase.**Diophantus's Arithmetica**. In Solar, give the slide rule to the Countess; she'll give this book to you in exchange. Put the book in the Living Room's bookcase.**Ars Magna**. In the Physician's Office, say`xyzzy`to open a hidden niche containing this book. (Note: This won't work until you've discovered the word by putting the square piece of metal on the parchment first.) Put the book in the Living Room's bookcase.**Finite-Dimensional Vector Spaces**. It's on the desk in the Professor's Office. Put the book in the Living Room's bookcase.**Principia Mathematica**. At Giant's Shoulder, return the toy mountain range to Newton; he'll give you this book in exchange. Put the book in the Living Room's bookcase.**Foundations for a General Theory of Functions of a Complex Variable**. Found at Complex: Modulus 1 and Acute Angle. Put it in the Living Room's bookcase.**Disquisitiones Arithmeticae**. Found at Gray Matter, Level Four when your score is at least 82. Put it in the Living Room's bookcase.**La Géométrie**. Found at Operator's Office, after you've rescued René Descartes from oblivion (see largest integer, correspondence, saying, and logic scroll). Put the book in the Living Room's bookcase.**The Art of Computer Programming**. It's inside the brown paper package found inside the mailbox at West of House. Put it in the Living Room's bookcase.**Liber Abaci**. The Count in the Great Hall gives this to you in exchange for some leaves. Put it in the Living Room's bookcase.**Fractals**. This book appears in the Living Room's bookcase when all twelve books that grant Mathematics Texts points have been put in the bookcase. Take it to any location on the complex plane (Real Axis: 1 is the closest such) and open or read Fractals there to win the game.

Papers:

- a
**note**. It's on your desk in your dorm room. Read it, but don't bother taking it. - a
**scrap of papyrus**. The acolyte tosses it into the urn in Temple of Number, Northern End. Read it. It's a clue on how to get past her. - a
**scribbled scroll**. At Hilltop, Euclid gives the scroll to you when you first greet him. Read it; it explains his postulates and problem. - a
**proof**. Found at "Irrational: Between 1 and 2". Take it to Temple of Number, Northern End and drop it. The acolyte will pick it up, read it, and leave, so she's no longer blocking your way to the Inner Sanctum. - a
**formal note**. It's on the low table in the Scholar's Study. Its "3.1415" signature is the clue you need to use with the buttons hidden in the study's wall designs, and you'll need some Geometry points to be able to find those buttons in the first place. - the
**trig homework**. It's at the Grassy Area. It contains a strong hint to look up logarithms in your math book. I think it's also partly meant to be a clue to put a wave into the phase inverter at Negative One. - a
**parchment**. It's in the Physician's Office. Put the square piece of metal on it to reveal the magic word`xyzzy`, which you should use in the Physician's Office. - a
**piece of paper**. It's sticking out of Pascal's pocket at Poker Game. You can take it, read it, and put it back, or just win the poker game and he'll drop it there when he leaves. The paper contains a copy of Pascal's Triangle from rows 0 to 10, conspicuously omitting the number that you need to tell the Count. - a
**pile of money**. It's at No Longer a Poker Game after you win at poker. Unfortunately, it's completely useless to you, although you can try giving it to the Count. - a
**thin card**. The farmer in the Barn gives it to you when you greet him. At Operator's Office, put the card in the slot to reconfigure the roller coaster into the curve that represents the equation on the card. Then`derive`the roller coaster; see toy mountain range. - a
**brochure**. It's at Roller Coaster Entrance. Read it to learn how the roller coaster is reconfigurable. - a
**logic scroll**. Achilles drops it in the Stadium after he wins a race against the tortoise. If Hypatia is at Window into Oblivion, ask her about Descartes, then show the correspondence, saying, and logic scroll to her in that order; she'll rescue Descartes and give you a crank. - a
**printout**. It's in the Research Lab. Read it. **Berkeley's lecture notes**. Berkeley leaves them behind in the College Hall.- Show the notes to Weierstrass in the Smoky Pub, then show him the limit shoes.
- Optionally, show the notes to Newton at Giant's Shoulder.
- some
**presentation slides**. They're in the Seminar Room. Read the seven pages one-by-one to get a better understanding of transformation matrices. This will help you use the equipment in the Research Lab. - a
**comic strip**. Found in the Neon-Lit Room. It's trying to tell you to pronounce "Euler" like "Yuler" and not like "Oiler". And it's also a hint that Euler has something to do with the bike puzzle there. **Descartes's saying**. It's in the Operator's Office. Take it. If Hypatia is at Window into Oblivion, ask her about Descartes, then show the correspondence, saying, and logic scroll to her in that order; she'll rescue Descartes and give you a crank.- some
**correspondence**. It's in the Operator's Office. Take it. If Hypatia is at Window into Oblivion, ask her about Descartes, then show the correspondence, saying, and logic scroll to her in that order; she'll rescue Descartes and give you a crank. - a
**wad of brown paper**. It's in your inventory after you open the brown paper package. It's useless. Discard it.

Shapes:

- an
**octahedron**. It's in the Inner Sanctum. Put the octahedron on the medium triangle pedestal in the Courtyard. - an
**icosahedron**. Kick the soccer ball in the Grassy Area to turn it into the icosahedron. Put the icosahedron on the small triangle pedestal in the Courtyard. - a
**cube**. It's in the Hidden Room. Put the cube on the square pedestal in the Courtyard. - a
**tetrahedron**. It's hiding in the pedestal underneath the globe in the Map Room. To reveal the tetrahedron, put Archimedes's staff in the gap and move the globe. Put the tetrahedron on the large triangle pedestal in the Courtyard. - a
**dodecahedron**. The poker table at No Longer a Poker Game turns itself into the dodecahedron when you try to leave the location. Put the dodecadron on the pentagon pedestal in the Courtyard. - a
**sphere**. Appears on the circle pedestal in the Courtyard when all five Platonic solids have been placed on their pedestals. Take the sphere to the College Chapel and put the sphere in the beam of light. This will animate the statue of Newton who will escort you to Giant's Shoulder where the two of you can have a chat.

Other stuff:

- a
**medicine bottle**. It's on the desk in your dorm room. Read it, open it, eat the pill that's inside, and discard the bottle. - a
**red pill**. It's inside the medicine bottle. Eat the pill. Then, holding only your math book, get on your bed and sleep. - a
**white wand**. It's in the "Void". Take it to "One" and wave the wand. You'll be incremented to "Two" and the wand will expand into the number line. - an
**old coin**. The Count in Great Hall gives it to you when you answer his math question:`tell count about 252`. This answer is clued by the triangle icon in the Castle Chapel and by looking up Pascal's Triangle in your math book. At Poker Game, after you've won a game of Two High in the Casino, put the coin on the table to play poker. (If you lose at poker, go back to Great Hall and ask the Count for another coin.) - a
**square root**. It's on a low table in the Scholar's Study. It lets you use the magic word`extract`in the number locations. - At Two,
`extract`to get to "Irrational: Between 1 and 2". - In the Physician's Office, with a negative wave in the mechanism, turn the crank to imbue the square root with negative energy.
- At Negative One,
`extract`with the negative-imbued root to get to "Imaginary Unit". - In the Smoky Pub, after both helping Weierstrass and visiting "Imaginary Axis: i", give the square root to Cauchy, who will augment the root's power.
- In Imaginary Unit,
`extract`with the augmented root to get to "Complex: Modulus 1 and Acute Angle". - In "69,105",
`extract`to escape back to "Irrational: Between 1 and 2". **Archimedes's staff**. Found at Inner Sanctum. Take it to the Map Room. Since you have a place to stand, put the staff in the gap and move the world (that is, the globe). This will reveal a tetrahedron in the concave top of the pedestal.- some
**exhaustion sandals**. Found at Inner Sanctum. - Try giving them to Achilles in the Stadium. Unfortunately, the sandals aren't quite good enough.
- Take Berkeley's lecture notes and the sandals to the Smoky Pub and show them both to Weierstrass (notes first, sandals second). Weierstrass will augment the sandals, turning them into limit shoes.
- a
**small coffer**. It's on the low table in the scholar's study. Unlock it with the tiny key. The coffer contains the white ring. - a
**tiny key**. It appears in the Alcove after you solve the the scales puzzle there. The key unlocks the small coffer. - a
**white ring**. It's inside the small coffer. The word "identity" on it is a clue to take it to "One". At "One", wear the ring to get to Zero. The ring will become a new part of the number line between Zero and One. - an
**empty set**. It's at Zero. It's your player's hold-all; put stuff in it. When it has something in it, it's just a**set**. You will explicitly need the set in order to carry some leaves. - a
**white framed mirror**. It's in the "Darkness" below "Gray Matter". Take the mirror to "One" and look in the mirror. You'll now be at "Negative One", and the mirror's frame will become the rest of the real axis, extending west from Real Axis: 0. - a
**slide rule**. It's at the Grassy Area. First look up logarithms in your math book to learn how to use a slide rule. Then give it to the Countess in Solar; she'll reward you with a wide-margined copy of Diophantus's Arithmetica. - a
**square piece of metal**. It's in the Physician's Office. Put the metal on the parchment to reveal the magic word`xyzzy`, which you should use in the Physician's Office. - a
**sine wave**, a**cosine wave**, a**negative sine wave**, or a**negative cosine wave**. These are the four forms of the same wave object. - The sine wave is first found by opening the panel of the mechanism in the Physician's Office.
- If you put the wave into the phase inverter at Negative One, it will be inverted. That means that a sine wave becomes a negative sine wave (or vice-versa) and that a cosine wave becomes a negative cosine wave (or vice-versa).
- If you
`derive`with the toy mountain range near a wave, it will be replaced with its derived curve. That means that a sine wave becomes a cosine wave, a cosine wave becomes a negative sine wave, a negative sine wave becomes a negative cosine wave, and a negative cosine wave becomes a sine wave. - If you turn the crank of the mechanism in the Physician's Office when a wave is inside its panel, the mechanism will briefly emit a burst of energy. It will emit positive energy if there's a normal sine or cosine wave inside, or negative energy if it's one of the negative waves inside the mechanism.
- If the square root is nearby when the mechanism's energy is emitted, it will absorb that energy. This alters how
`extract`works. Normally, you can only extract a square root when at a positive number, but when the root has negative energy, you can extract the square root at "Negative One" to be rotated to "Imaginary Unit". - a
**toy mountain range**. Given to you by Newton himself at Giant's Shoulder after answering a few questions correctly. You can now use the magic word`derive`to convert all nearby curves (that are expressable inform) into their derivatives.*y*=*f*(*x*) - You can
`derive`the sine wave to a cosine wave, then that to a negative sine wave, then that to a negative cosine wave, then that back to the sine wave. This is interesting but not necessary. - You can
`derive`the roller coaster into a new curve. You'll want to put the thin card into the slot at Operator's Office, then`derive`the resulting coaster. - On the derived coaster, use the
*x*-finder; see*x*-finder for details. - Return the range to Newton at Giant's Shoulder; he'll give you a copy of Principia Mathematica in exchange.
- an
. It's in the Operator's Office.*x*-finder - First, setup the roller coaster so it represents the derivative of the farmer's equation; see thin card and toy mountain range.
- Remove the plastic film from the finder so it is no longer waterproof.
- At Boarding Platform, attach the finder to the loop of the car.
- Enter the car; the
*x*-finder will now have the value of the curve when the car hit the water. Since the waterline represents 0, and the coaster was the derivative of the farmer's equation, and 0 on a derivative corresponds to the maximum value of the original curve, therefore the finder's value has the maximum desired value for the farmer's equation. - Give the finder to the dog in the Barn. He'll return with the farmer and you'll earn 7 points in Calculus.
- a
**wad of plastic**. Obtained by removing the plastic film from the*x*-finder. The wad of plastic itself is useless. - some
**limit shoes**. Obtained by giving Berkeley's lecture notes and the exhaustion sandals to Weierstrass in the Smoky Pub, in that order. - Give the shoes to Achilles at Stadium. He'll win his race, return the shoes to you, and drop the logic scroll.
- Wear the shoes from now on. You'll need them on when using the Machine Room.
- Go to Machine Room. Set the controls to an appropriate combo (eg: Identity Series) so when you go south, you reach Infinity.
- Return to Machine Room. Set the controls to the harmonic series (Reciprocal Series) and go south to Infinity again to impress Ramanujan.
- Return to Machine Room with the brass rod. Put the rod in the hole, set the controls to Alternate Reciprocal Series and go south to reach "69,105".
- a
**spare key**. It's in the desk drawer in the Professor's Office and it unlocks the door into (or out of) the office. - the
**largest integer**. Obtained by taking the nothingness twice at Infinity. Put it on the tray at Window into Oblivion to summon Hypatia. - a
**small crank**. Hypatia gives this to you at Window into Oblivion after René Descartes is rescued. You'll need to use the transformation matrix in the Research Lab to flip the crank into its mirror image: set the switches to 0 1 0, put the crank on the platform, and push the button. Go to West of House and put the crank in the hole of the mailbox, then turn the crank to open the mailbox. (If you mess up the crank's transformation, take the crank to Window into Oblivion and knock on the door. Hypatia will give you a new crank.) - a
**brown paper package**. Found in the mailbox at West of House; see small crank on how to open the mailbox. Open the package to get a wad of brown paper and a copy of The Art of Computer Programming. - a
**brass rod**. Found in the Grand Court after you've solved the Grand Hotel's puzzle. Put the rod in the hole in the Machine Room. Set the controls to Alternate Reciprocal Series, then go south while wearing the limit shoes to reach "69,105". - some
**leaves**. Found in "69,105". You'll need the set to be able to pick them up. Give them to the Count in Great Hall; he'll reward you with a copy of Liber Abaci.

`You estimate that you would score your-score out of 100 on tomorrow's final, broken down by the following subject areas:`

`Algebra: 8/8`

- 4 points for solving the scales puzzle in Alcove.
- 4 points for opening the chest in the Hidden Room.

`Arithmetic: 5/5`

- 2 points for reaching "Point" for the first time.
- 1 point for reaching "Positive Axis: 2" for the first time.
- 1 point for reaching "Beginning of Positive Axis: 0" for the first time.
- 1 point for reaching "Number Line: −1" for the first time.

`Calculus: 10/10`

- 3 points for answering all of Newton's questions correctly.
- 7 points for solving the farmer's barrel puzzle.

`Combinatorics: 8/8`

- 3 points for solving the Count's puzzle.
- 5 points for solving the bike ride traversal puzzle.

`Complex Numbers: 4/4`

- 2 points for reaching "Imaginary Axis: i" for the first time.
- 2 points for going up from "Complex: Modulus 1 and Acute Angle" for the first time.

`Cryptography: 2/2`

- 2 points for discovering the magic word XYZZY.

`Geometry: 10/10`

- 3 points for solving Euclid's postulates problem.
- 5 points for taking the Platonic Solids; 1 point per shape.
- 2 points for putting the Platonic Solids onto their pillars.

`Infinity: 8/8`

- 2 points for helping Achilles win his race with the tortoise.
- 2 points for reaching "Infinity" for the first time.
- 2 points for helping the Grand Hotel clerk solve his problem.
- 2 points for reaching "69,105" for the first time.

`Linear Algebra: 7/7`

- 4 points for entering the Professor's Office for the first time.
- 3 points for transforming the crank into its mirror image.

`Logarithms: 4/4`

- 2 points for looking up logarithms in your math book.
- 2 points for giving the slide rule to the Countess.

`Logic: 4/4`

- 4 points for rescuing René Descartes from oblivion.

`Mathematics Texts: 12/12`

- 12 points for putting mathematics textbooks in the bookcase; 1 point per book.

`Number Theory: 5/5`

- 3 points for solving the primes puzzle in the Librarian's Office.
- 2 points for reaching "Irrational: Between 1 and 2" for the first time.

`Physics: 4/4`

- 2 points for using a staff as a lever to move the globe off its pedestal in the Map Room.
- 2 points for refracting white light into a rainbow in College Chapel.

`Probability: 6/6`

- 4 points for winning the Top Two arcade game in the Casino.
- 2 points for winning at poker.

`Trigonometry: 2/2`

- 2 points for inverting a wave.

`If you remember your professor's grading scale correctly, this would earn you a(n) grade in the course.`

Grades:

`F−`*(0 points.)*`F`*(2 to 18 points.)*`D−`*(22 to 23 points.)*`D`*(27 to 34 points.)*`D+`*(39 points.)*`C−`*(41 to 42 points.)*`C`*(46 to 51 points.)*`C+`*(56 to 58 points.)*`B−`*(61 points.)*`B`*(68 to 71 points.)*`B+`*(75 to 79 points.)*`A−`*(81 to 83 points.)*`A`*(85 to 99 points.)*`A+`*(100 points.)*

This walkthrough was funded via Patreon with

- the support of Thomas Bøvith, Christos Dimitrakakis, Darius Katz, Ville Lavonius, Andrew Schultz, Jacques Frechet, Kenneth Hon, Jason McIntosh, Mark Musante, and Phil Tatro;
- the generous support of Janice M Eisen and Karl Ove Hufthammer;
- the
support of Emily Short, Allen Garvin, Jesse McGrew, Jacqueline Ashwell, and Marius Müller;*extremely generous* - and the invisible support of several anonymous patrons.