Posts Advent of Code 2021

Advent of Code 2021

A collection of Mathematica programs and rhymed poetry written for Advent of Code 2021. Highlights include a ten-page cave-diving text adventure game poem and the confessions of a polymer scientist.


This repository stores my Advent Of Code solutions for 2021, written in Mathematica. I’m using .wls instead of .m, and trying to make the code somewhat readable as plaintext, but casual Mathematica in general is notebook-heavy, and isn’t great to view on GitHub in any format, so it’s not perfect.

Though there’s no specific subreddit challenge this year, I also wrote a poem for each day’s problem, as shown below. I tried not to repeat the same rhyme and metre scheme too much (and avoided iambic pentameter sonnets, since I used them as a crutch last year and the year before), but ultimately had to repeat a few by the end.

Days Completed

Click on any of the day #s to see the problem for that day, and on any of the titles for my code.


Day 1: Stalling the Seven Seas

Today, we lost the sleigh keys on the ocean:
A tragedy we’ll need a month to right.
They’re truly lost; we haven’t got a notion
Of where they got to after leaving sight.
And so from duty verging on devotion
We’ll start our month-long enterprise tonight.
We certainly won’t rummage in slow-motion…
(…okay, we just like submarines, alright?)

We’ll need a month, at least, to find the keys
Which, sadly, we misplaced beneath the seas.

Day 2: Run Silent, Run Deep

The water here is mighty cold,
And more pitch black than tar.
The vales are deep, or so we’re told,
But we have got a star.
We don’t know what day 3 will be,
Or what errand it tells,
But our floodlights are green and red.
Our sonar’s jingle bells.

The challenges we’ve done before
Have rarely been a burden.
(Like inverse mods; I’d like some more
If I could get a word in).
It’s difficult to cry or pout,
When we can hear a sleigh,
And “Silent Night” is sung about
The Christmas on the way.

Day 3: The Power of Two

One and zero: the only components
Of your hardware, on closer review.
It can calculate monstrous exponents,
With transistors that can’t count to two.

With just one piece - the primitive NOR gate -
You can process the bits that pass through:
Turning on for the offs at the door gate;
And for ons there, returning untrue.

You can turn NORs to XOR gates and ANDers,
And inverters, to name just a few.
And the multi-bit adder-expanders,
Are sufficient to build ALUs.

From these pieces are made all our widgets;
It’s astounding just what they can do.
You can build a whole world with two digits:
“On” and “off”; that’s the power of two.

Day 4: There Was a Sub That Had a Squid

Across and down,
You count to five;
You fear to drown,
But you’re alive.

The squid is big
Enough to hew,
Like one small twig
Your sub in two.

It wants a show
And you’ve the thing
Which ends in ‘o’
And starts with ‘bing’.

It makes a bet
And you agree
(You’ve racked some debt
Out here at sea).

It weighs a ton,
Your questioned sin:
Should it have fun,
Or should you win?

You’ve rigged the boards,
So now, you think:
What use rewards
If then, you sink?

Day 5: Crossing a Line

With lines of toxic vents below,
We make our map, and off we go.
They’re deadly when they intersect
But we won’t cross those lines - we’ve checked.

We tidy up our code with Sign[]s,
To handle all the types of lines.
And then we read the code and scout
For useless lines, to cross them out.

And cleaning up the code, we find
That most of it can be un-lined:
The hash maps? Gone. And same with Do[].
Non-function lines? Cross them out too.

The cleaning’s fun, the code is neat,
But timewise, I’ve been soundly beat.
Code fast and well? I’m at a loss;
That line is always hard to cross.

Day 6: Multiply

It glows
And grows
Then slows
In throes.

Then two fish swim.
They start out slim
But things look grim:
There’s four of ‘em!

The school of four fish, swimming past
Began with one; three more amassed
And still they’re replicating fast
There’s eight; I hope we’ve seen the last.

Now, if the lanternfish could die, or if they needed food or clothes,
Then things might never go awry, if they were limited by those.
A normal fish will say good-bye, but not (it seems) the fish that glows.
I’m scared about this school, for I just counted sixteen; still, it grows.

Day 7: The Crustacean Supplication

Crabs above whose sea we scuttle
Give us aid, and not rebuttal,
Danger comes, surpassing cuttle:
Blast a hole, and don’t be subtle!

We’ve made friends with a crustacean
Stacking cups while on vacation,
After games of long duration:
Save us from this huge cetacean!

Whales are fast; too late we tracked them.
Bingo, too, does not distract them.
Submarines, like ours, attract them:
Save us, or they’ll soon have snacked them!

Hurry, blast through sheet and shale!
Wale away, away from whale!
It’s almost here! We must not fail!
Grant us weal lest we should wail!

Day 8: Constraint Problem

The caves and segments both constrain
Where we are apt to go,
And like the tracks that turn a train
Our course is set, we know.

Constraints leave but a single route:
The segments made it clear.
So since we’re stuck until we’re out,
I hope the keys are here.

Day 9: Lines Inscribed on a Utilities File

Though we prepare for puzzles there
Are errors we cannot prevent
Within the code that we have stowed
Throughout the year for this event.

And when we try to re-apply
These functions that we wrote before,
The syntax breaks like mica flakes
And errors fill the screen, and more.

The cost is sunk (or so we’ve thunk)
And wasting Utils causes pain,
So we debug, no longer smug,
And lose the time we thought to gain.

But in the end, we do amend
And make it through this game we play.
We coders are, to get each star,
Like broken clocks, right twice a day.

Day 10: Luck is the Draw

“So you see, we keep score,”
Said the checker, explaining,
“It can be a chore,
But it’s quite entertaining.”

I looked back, quite confused,
At this odd explanation.
Were they that amused
By some syntax mutation?

So said I, in responding,
“Your scores are all random!
They’re just corresponding
To letters in tandem!

In what way is it fun?
You’ve no choice in the outcome!
So I won’t say it’s ‘dumb’ -
But you’re smarter without some!”

It looked taken aback
When I finished my question,
Despite my clear lack
Of a better suggestion.

And it thought long and hard
About how to explain it;
If it gave some canard,
I’d be sure to disdain it.

And at last, it was done,
To explain their desire:
“You see, if you’ve won,
There’s some stars you acquire.”

Day 11: Dumbos

These octopuses aren’t so bright, but yet they get to shine,
And light the caves for miles around when energies align,
Eventually syncing up, converging by design:
Their pastimes seem to go an awful lot smoother than mine.
And so, when yet another piece of submarine should break,
I envy the dim octopi; machines were a mistake.

Day 12: All Roads Lead To Home

By far my longest poem; written over the course of about five hours from my real input map. Click the link below to see the map if the embedded image doesn’t load.

PRO PATHFINDER: Choose your path wisely

PRO PATHFINDER: Choose your path wisely.

Welcome to PRO PATHFINDER v. 1.0!
Please enter your name:

Begin y/n?
> y
Loading `start`...


Welcome, DIJKSTRA, to your quest.
Journey onwards, if you dare.
Choose now: south, or east, or west?
Dangers dwell within: beware!

Caverns you may visit twice,
Or more, as heart and path inclines.
Small caves, one visit must suffice!
Never twice to those confines.

Do you seek to leave these caves?
Reunite with folk and friend?
Sally forth, and use your saves!
The passage that you seek is end.

Dare you, DIJKSTRA, now to start?
Pick between your choices three.
You have the map. Have you the heart?
GW, nx, pt?

> GW
Loading `GW`...

Gnome Wizard

“Welcome, DIJKSTRA,
To my home!
I am wizard.
I am gnome!

“You may leave
Or you may wait.
I am wizard.
I am great!

If you’re hurt,
I’ll fix you up.
I am wizard,
Here is cup!

sx? nx?
lg? ve?
I am wizard,
Tall as knee!”

> take cup
You take the cup.  Inventory contains: cup.

> sx
Loading `sx`...

Sinking Xanadu

In Xanadu did Kubla Khan,
A stately pleasure-dome decree.
Where Alph, the sacred river, ran
Through caverns measureless to man
Down to a sunless sea.

But we have measured now, and well
We know the routes and paths and ways.
And long ago, the tunnels fell,
With mournful noise, as though a knell
To sound our end of days.

Hark now! The final Vespers chime!
The way from whence you came shall heave.
Flee to GW in time
Or perish here, like Coleridge’s rhyme.
Leave now, or never leave!

> GW  
Loading `GW`..  

Gnome Wizard

“Ahh, welcome back!
You made it out!
That Xanadu’s
A tricky route.

I’m glad you’re safe!
I’m glad you’re here!
That way is gone.
Won’t reappear!

nx is nice,
Or so I’ve heard.
lg? ve?
They’re not preferred.

I’ve seen your fate:
We’ll meet again.
I am wizard!
See you then!”

> nx  
Loading `nx`...  


You have come to the spot in the center,
Where the passages all intersect.
There are five different ways you can enter.
There are four different paths to eject.

You may go to GW’s wizard.
You may go to SM’s clever horse.
Or pt, where the siren’s call is heard.
Or lg, where the lamprey has force.

But although your quaint drawing connects us
There is still one unbreakable rule:
You can never come back to the NeXus,
So choose wisely, and don’t be a fool.

> pt  
Loading `pt`...  

Perfect Tune

“Oh, DIJKSTRA, praises be that you have come!
I knew you’d make it, but I’ve waited long.
Beyond that door, the Alph is sailed and swum,
And there, my sisters sing - listen! Their song!”

> press cup to door  
You press the cup to the door.  
> press ear to cup  
You press your ear to the cup.  You can faintly make out the words...  
Suddenly, you are struck with an irresistible urge to get closer!  
Battering down the door, you dive into the water. 
Soon, you find yourself swept away by the current and dashed upon the rocks!  

You have fallen prey to the sirens!  
Undo y/n?  
> y  

> wait  

“You dare to mock my wait? My sisters’ hymn?
You won’t give heed to music in the air?
You won’t go in the Alph with me to swim?
SM, or else uq, then! I don’t care!”

> uq  
Loading `uq`...  

Ultimate Question

“I see you’ve come to me at last;
So please, do sit and stay.
The question that has puzzled me
Is clarified today.

I am the Great Computer
And I’ve waited here for thee
To arrive and act as tutor.
For this question and for me.

It has gnawed at me like cancer
But solutions here you bring.
So, pray tell, what is the answer
When one questions everything?”

> 42

“…so simple. So sublime. Indeed,
And beautiful, it’s true!
I have the final piece I need
My answer: Forty-two.

So in return, I warn you now:
Do not go to TG!
SM is now your only choice.
I help, as you helped me.”

> TG
Loading `TG`..

The Game

You have lost the game!
Undo y/n?
> y

Ultimate Question

> SM
Loading `SM`...


“I am the horse who lives beneath the sea.
Of FACTS and LOGIC do I make my home.
You Yahoos all look just alike to me;
I am a Houyhnhnm beneath the foam.

Your trial states that you may here return
But logically, I doubt you ever shall.
If you can’t see this, you have much to learn,
ve, or else lg via canal.

You could, of course, directly go to end,
But I know DIJKSTRA takes excessive risk.
Unlike the wizard, I am not your friend,
But when you see the Guardian: be brisk!

> lg
> Loading `lg`...

Lamprey Guardian

Through mud
I scud
For blood.

For eel
This meal
Is real.

I’ll drink
Your ink,
I think,

And feed
With speed.

> GW
Loading GW...

You flee
From me,
I see…

Gnome Wizard

“Here at last!
You’re still alive!
There were odds out:
Six to five!

I see you’re hurt.
A lamprey bite?
I am wizard!
I’ll make right!

All better now?
You see, I fix!
I am wizard!
I have tricks!

There’s just one path
As you can see:
No more options!
Pick ve!

And when you leave,
I’ll sit and cry.
I am wizard!
Now, goodbye!

> ve
Loading `ve`...

Very Easy

Threre are three different jugs on the table,
Which, to pass, you must fill by a reckon.
Now, the first jug is filled with eight cups’ worth,
But just five cups will fit in the second.

Now, the third has three cups as its measure,
But is empty now, just like jug 2.
So with eight cups’ of water between them,
Here’s the puzzle presented to you:

Via pouring these jugs, move the water,
So the first jug is half full with four,
And another four cups in the second,
And the third must be empty once more.

Hearing this, do you think you can do it?
Can you finish before you’ve turned grey?
You have journeyed twelve days underwater,
But I think that much longer you’ll stay.

> inv
Inventory contains: cup.
> scoop water with cup
You measure out a cup of water - sure enough, you can scoop exactly one cup's worth!
You begin scooping water from the large jug one cup at a time.
Soon, you reach the configuration [4, 4, 0].

You have cheated! No fair! That’s illegal!
I should never have trusted the gnome!
I can’t stop you - the end is now open,
So although you’ve not earned it - go home!

> end
> Loading `end`...


Well done, DIJKSTRA! Here’s the end.
Roads are tough, and travels, long.
Trips like yours will soon be penned:
Your journey will sound good as song.

Traveling to every room
You’ve kept the rules down to the letter.
Narrowly avoiding doom
And every time, returning better.

Though you’ve won, if you should want
To try a slightly harder mode
In which you can - just once - re-jaunt
That trip would surely earn an ode.

If you should care to try again
And come back to a fresh debut,
Eject the floppy disk and then

Day 13: Origami

Gossamer paper
Folds to make complex patterns
Like Christmas snowflakes.

Day 14: Confessions of a Polymer Scientist

Long ago, I was free;
When no chain-links bound me,
I was filled to the brim with elation.
But I branched out - alas! -
To the plastics and glass
In the realm of polymerization.

I had dallied, of course,
With the Circle of Mohr’s,
And with chemistry had a flirtation.
But I dodged every hook
‘Till I picked up a book:
“Painter-Coleman: Polymerization”.

When I started this school,
I thought resins were cool
Since the heat was not set to “cremation”.
But when temps went ablaze
I was set in my ways
By the thermo-polymerization.

Yes, I’ve long since been cured
Of atactic which lured
Me to radicalize my vocation.
But, I cannot change gear
Since I’ve made my career
In this field of polymerization.

I have given some talks
To Electro-Chem docs:
They enjoy every graph and citation,
But the adjuncts are mean:
“That’s spaghetti on screen!”
When I show them polymerization.

But there’s upsides as well
To the field where I dwell:
I don’t need Maxwell’s stinking equation!
For my stuff can’t conduct
And electrons get chucked
Out the door in polymerization.

There are others out there
Who I’ve linked with to share,
And our network’s helped ease the frustration.
Meeting people like me
Has increased my degree,
My degree of polymerization.

And I’ve even had fun
Letting DSC run
While I’m counting chain ends with titration.
And in fact, if compared
To compilers, I’m scared
Since my program’s not spared
From the errors declared
Which all must be repaired
By a man unprepared –
So I’ll stick to polymerization!

Day 15: Lazy Limerick #1

You can pathfind to dodge all the critters
But the coding is not fit for quitters.
By the time you have won
When you’ve got it to run
I won’t blame you for getting the jitters.

Day 16: An Ordinary Conversation

“Ahoy! Is this the submarine?
Our packets should be nigh.
Can anybody hear us? Do you copy? Please reply!”

“A scrambled mess was all we got
Of data clearly hexed.
Could you be just a bit more clear? We’re all a bit perplexed.”

“A packet’s version number, then it’s
Operator, ID,
Concluded by the subpackets. It all is rather tidy.”

“And when we’ve done recursion, while more
Obstacles befall us?
Come on and say the matter where you couldn’t simply call us!”

“Any math, we send to you,
Or else, it’d surely bore us.
Class had homework overdue we’d hope you’d figure for us…”

Day 17: Cast My Words Into The Ocean

Inspired by /u/CCC_037’s solution in the programming language Rockstar. This is in no way a valid Rockstar program.

Let my time be not my time.
Let verses carry thought.
Cast meaning into poetry.
Let target be the spot.

Shatter coords into shreds;
Cast x into the sky.
If x stops rolling short of goal
Then never think of why.

Rock the system with the x.
Rock on, and rock again.
Until the target is surpassed
Rock on; but roll it then.

Take the target - why the start
While target lacks a care?
Upend the target utterly.
Why should it finish there?

Every coord now will soar
Until the sky is furled.
Count targets struck by poetry.
Shout highest. Shout the world.

Day 18: Lazy Limerick #2

There’s a new way to finish your mission:
You must implement snailfish addition.
There’s a Split[] and Explode[]
In Reduce[] in your code;
Do it fast, and you’ll seem a magician.

Day 19: A Beacon in the Veil of the Night

How can we travel safely through this cold expanse of night,
With disconnected beacons as the only source of light?
The scanners that the probe released don’t know their East from West.
They share a dozen beacons, sometimes; we will do the rest.

With mirrors, there are forty-eight directions and rotations
For each potential overlap between a pair of stations.
For all six faces on the cube, we pick the beacons closest,
For both beacons, that comes to six times twice a gross (a grossest?).

Should both the lists of beacons from each scanner be re-sorted,
Then for one combination, there’s a lone difference reported.
This difference is the offset; all we need to join the patches
Is check a dozen dozen dozen candidates for matches.

The order is beyond quadratic; code is beyond slow,
But patience is enough to make these ocean trenches glow:
When each and every scanner has another in its sight,
Then we will fill the murky depths beneath the waves with light.

Day 20: Zoom & Enhance

Hold it. Run that back, half speed.
Go forward three more frames. Advance.
Right there - that glint is what we need,
So zoom in there. Good. Now, enhance.

These algorithms reconstruct
And pierce through graininess and gloom
That, on first sight seem to obstruct
A photograph. Enhance it. Zoom.

The glint is a reflection from
A polished doorknob, and by chance
The perp just into view had come;
Uncrop the image, and enhance.

No luck. His face still can’t be seen.
‘Twas blocked by someone in the room.
But look! Those pixels there, in green!
An eye, an iris! Pan there! Zoom!

We too can see the things she saw
Reflecting off her forward glance
I see a nose and upper jaw:
Enough to find a face. Enhance.

Have eigenvalues locked on target?
Good work. Bitmap, then resume.
Our fractal codes (a bit of argot)
Databased a match. Now, zoom.

Investigations once depended
Far too much on cirmustance.
With these tools, those days have ended.
Thank you, code! Now, zoom. Enhance.

Day 21: The Garden of Forking Paths

You saw a flower on the left
Too lovely not to look.
I drifted rightward, from the heat
To find a shady nook.

And from that point our paths diverged
And separately we strolled
Throughout the garden of the worlds
Where trees and dice are gold.

Each garden path, past vine and root,
Continues into three,
But here and there two paths will meet,
Rejoining from the tree.

I wander through the many paths,
And smile at the flowers,
And pretty things that bring to mind
Old memories of ours.

But never do I stop and linger
Longer than a minute;
This garden with its endless green
Has one more flower in it.

And so I walk the myriad paths
And roll old Dirac’s dice,
Until we meet, and hand-in-hand
Can walk through Paradise.

Day 22: Cube

With length and width and height,
Complexity is cubic.
Brute force won’t work tonight,
Much like the cube of Rubik.

I’ll code it up in Rust
(Mathematica by proxy).
The leaderboard’s a bust.
My brain is feeling boxy.

Day 23: Walking Through The Room

Sung to the tune of a song by The Police.

Tiny steps are what you take
Walking through the room.
Don’t shuffle a mistake
Walking through the room.
Amphipods in hallways
Walking through the room,
Can’t arrange in all ways
Walking through,
Walking through the room.

Some may say
“Store amphis in an array.”
No way.
Got structures to use today!
Some say
“Code’s too hard, by hand’s the way!”
It may
But I may as well play.

Tiny steps are what you take
Walking through the room.
5 AM and you’re awake
Walking through the room.
Amber, Bronze, and Copper
Walking through the room,
Get ‘em sorted proper
Walking through,
Walking through the room.

Some may say
“We’re not getting keys for sleigh.
No pay
If we’re not back Christmas Day!”
Some say
“Just leave ‘em in disarray”,
But nay:
We may as well play!

Day 24: Logic

Me and logic parted ways,
Our friendship at an end,
For forcing me to think, on days
That I did not intend.

Now, though, I have huge arrays,
And digits to append.
Logic I won’t stop to praise.
Brute Force, though, there’s a friend.

Day 25: De Profundis

Into the depths we dove, into the sea,
Past lanternfish and amphipod and whale,
To find, beneath the cucumbers, the key
Which sank beneath the waves, over the rail.

Into the depths we delved, into the code,
Aligning beacons, counting all the paths,
Polymers, and dice (when we had slowed),
And helping out some snailfish with their maths.

Into the depths we ducked, behind the scenes
Where Eric and the mods concocted fun,
To keep us in good cheer till we’d the means
To surface once again and see the sun.

Clavis Davidica unlocks the way,
And brings us, from the depths, home Christmas Day.

This post is licensed under CC BY 4.0 by the author.