HOLIDAY PUZZLE 2025!

Gabrielle Birchak/ December 9, 2025/ Ancient History, Enlightenment, Future History, Uncategorized

UPDATE!! AS OF DECEMBER 18, NO ONE HAS SUBMITTED CORRECT ANSWERS! SO THANKS TO DAVID T. AT ASU, THE PUZZLE HAS BEEN GIVEN AN EXTENSION TO DECEMBER 31, 2025! 

Wel­come to Math! Sci­ence! His­to­ry! It’s Decem­ber and that means it is Puz­zle Month. Hi, I’m Gabrielle Bir­chak. I’m a sci­ence com­mu­ni­ca­tor with a back­ground in math, sci­ence, and jour­nal­ism. This year, we are mak­ing up for the last cou­ple of missed puz­zles, so we’re hav­ing a two-parter. So stick around after the mid­point. The sec­ond puz­zle relies on the answers from the first puz­zle, so make sure you get some good notes. And when you are com­plete­ly fin­ished with the entire puz­zle next Tues­day, send us your work and results. Yes, show your work, no cheaters, no pump­kin eaters. The first place win­ner is the one who answers it first and cor­rect­ly. You will receive an Ama­zon gift card for $25 and some math sci­ence his­to­ry mer­chan­dise. The sec­ond place is for the per­son who answers it sec­ond and cor­rect­ly, and they will win some math sci­ence his­to­ry mer­chan­dise. And the third is for the per­son to get it in just on the dead­line. Third place win­ner receives one of our lat­est com­put­er stick­ers. We think you’re gonna like them. 

So get out your trusty notepad, take some dili­gent notes!

The year is 2525 and you are a Chrononaut, a time trav­el­er, an agent of tem­po­ral cal­i­bra­tion and inter-cen­tu­ry intel­li­gence. This hol­i­day as you get ready to enjoy the time with your fam­i­ly you receive a call from the bureau. You go into your office know­ing that you will be back before din­ner, and you are imme­di­ate­ly trans­port­ed into head­quar­ters, known as The His­to­sci­en­ti­math­i­cal Bureau, the intertem­po­ral agency for the safe­guard­ing of all math­e­mat­i­cal, sci­en­tif­ic, and his­tor­i­cal integri­ty.

Your Chrono Team Leader for Earth, Veron­i­ca, meets you at the door and walks you to your cap­sule. Her eyes glow a beau­ti­ful sooth­ing green, that light the path before you through the hall­ways at head­quar­ters, cre­at­ing a soft-green light on the floor. It’s offi­cial. You’ve been green-lit.

VERONICA:

Wel­come, Chrononaut. Sor­ry to pull you away from your fam­i­ly dur­ing the hol­i­days but we have acti­vat­ed you from sta­sis with Lev­el Three clear­ance. We are send­ing you on two mis­sions with six loca­tions. Time anom­alies have dis­rupt­ed the sequence of knowl­edge. You must recov­er sev­en keys, these are frag­ments scat­tered across space-time. These keys will sta­bi­lize the Con­tin­u­um. You will need to solve the sequence, decode the num­bers and realign the past. You will take the first mis­sion to find the first three keys.

Veron­i­ca says as she points to your cap­sule. You step in and turn around to look at her.

VERONICA: We are count­ing on you to sta­bi­lize the time­line before a knowl­edge-col­lapse rip­ples across the cen­turies. We wish you safe trav­els. Track your cof­fee rations. Your cos­tumes are hang­ing up in the bathroom.

The doors close. You sit at the helm. The lights dim, and the walls pulse to the voice that tells you your first mission: 

CAPSULE: Tem­po­ral inser­tion one: Send­ing you to Alexan­dria, Egypt, in the Earth year 395 BCE.

And in the blink of an eye, you arrive out­side the great Library of Alexan­dria. You gear up with your toga and bag, found in the bath­room, of course, car­ry­ing your trusty notepad and pen­cil. As you enter the library, you see scrolls that tow­er to the ceil­ing. Scribes whis­per across the sun­lit court­yards. The air smells of ancient ink, pressed papyrus, and curi­ous­ly, roast­ed beans. A schol­ar in a pur­ple linen robe approach­es you.

With­out a word, she greets you and walks you to a hall­way. You are both being fol­lowed by a beau­ti­ful desert cat that appears to be chas­ing a lit­tle red dot. You enter the hall.

It has 12 cub­bies, each filled with one scroll. Your guide speaks softly.

HYPATIA: Some say knowl­edge begins in chaos, but this pat­tern has always whis­pered order.

The schol­ar offers you a steam­ing clay mug. The scent is strange­ly familiar.

HYPATIA: Import­ed. A rare bean from the moun­tains beyond Nubia. Helps with sequences.

You take a sip. That is some good cof­fee! She turns and walks away. Could that have been the great Hypa­tia? You turn back to the cub­bies. You reach for the first scroll, care­ful­ly unrolling it.

It has only one num­ber on it: The num­ber 1.

You reach for the sec­ond scroll. Again, it has only one num­ber on it: The num­ber 1.

You go through each scroll, writ­ing down the num­bers from each scroll:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, _____

Final­ly, you get to the twelfth cub­by, and pull out the last scroll. In faint, char­coal ink it reads, 

“Fill in the next val­ue. The 12th num­ber. When you do, the Fibonac­ci Gate opens.  And you may  continue.”

🧩 PUZZLE INSTRUCTIONS

You’re look­ing at a Fibonac­ci sequence: each num­ber is the sum of the two before it.

What is the twelfth num­ber in this sequence? Cal­cu­late it care­ful­ly. There is only one cor­rect answer. This num­ber becomes the first key in your mis­sion. Sub­mit your answer as a whole num­ber. No esti­ma­tion. No rounding.

You write down the answer in your notepad, close it up, and walk out to your cloaked capsule.

You walk in and sit at the helm. The cap­sule dark­ens, and the walls pulse with the voice in the capsule.

CAPSULE: One key secured, two more await. Stand by for your next jump, Chrononaut. Stand by, Chrononaut. Your next inser­tion point is confirmed.

Your cap­sule arrives in a snowy field with a large stone estate in the dis­tance. You ask your com­put­er where you are. The com­put­er replies.

CAPSULE: You have arrived in France, in the Earth year 1740, dur­ing the Enlight­en­ment.
Tar­get: Gabrielle Émi­lie Le Ton­neli­er de Bre­teuil, also known as Émi­lie du Châtelet, the physi­cist, philoso­pher, math­e­mati­cian… and, unof­fi­cial­ly, the rea­son the His­to­sci­en­ti­math­i­cal Bureau had to revise its “No Time-Entan­gle­ments with His­tor­i­cal Genius­es” clause. Please remem­ber that the His­to­sci­en­ti­math­i­cal Bureau would like to empha­size that field agents are no longer per­mit­ted to quote Émilie’s let­ters aloud after Time­line 6‑A col­lapsed into a rhyming loop.

Well, that’s inter­est­ing, you tell your­self. No-time entan­gle­ments, what does that mean? So you go to the bath­room, and there it is, your Roco­co attire, com­plete with ruf­fles and silk.

You grab your note­book and pen­cil, stuff it into your silk tote, and haul across the snowy field in your tight and uncom­fort­able buck­led leather shoes. You mum­ble to your­self, mak­ing note that the Bureau needs to pro­vide prop­er-sized shoes for these kinds of expe­di­tions. After being escort­ed down a grand hall­way, you arrive inside her study.

Warm despite the snow out­side, books in Latin and French are stacked like ram­parts around the hearth. New­ton’s Prin­cip­ia sits on one large table with a cracked teacup beside a stack of can­dle-stubbed note­books. Snow taps gen­tly on the frost­ed glass.

At this time in Earth his­to­ry, Emi­lie is the first woman to have pub­lished a paper with the Roy­al Acad­e­my of Sci­ences in Paris. Emi­lie, wear­ing a silk sky-blue robe over her hooped dress, sips from a porce­lain cup. Stand­ing at her chalk­board, she taps her foot.

The board is cov­ered in sweep­ing inte­grals. With­out even look­ing at you, she says,

EMILIE DU CHATELET: Chrononaut, I assume you’re here for the falling object problem?

You walk over to her. She taps her chalk against two fresh­ly writ­ten formulas. 

The top one reads,

s(t)=4.9t^2

And

v=v_0+at

EMILIE DU CHATELET: While I was vis­it­ing the Cliffs of Étre­tat, I dropped a stone. These equa­tions tell me how far it falls, in meters over time. In these equations,

t = time\\
a = acceleration\\
v = velocity\\
v_0=the\ initial\ velocity\ of\ the\ rock

EMILIE DU CHATELET: Tell me, how fast is it falling exact­ly three sec­onds after I let it go?

She rais­es one eye­brow. She smirks at you and takes a sip. Her but­ler pours a sec­ond cup and brings it to you.

EMILIE DU CHATELET: No approx­i­ma­tions and no short­cuts. That is Bureau Blend. Strict­ly speak­ing, the His­to­Sci­en­ti­Math­i­cal Bureau pro­hibits the con­sump­tion of twen­ty-sixth cen­tu­ry stim­u­lants across time­lines with­out a Form 9e, but I won per­mis­sion in a pok­er game with the Com­man­der of the Chrono­fold. Don’t wor­ry, you have per­mis­sion to break the law here.

And she winks again.

“Wait, you met the com­man­der?” you ask.

EMILIE DU CHATELET: I did. He has a thing for fold­ing laun­dry and dri­ving twen­ty-first cen­tu­ry elec­tric vehi­cles. He even taught me how to dri­ve one. It sure took the thrill out of our horse and bug­gies. By the way, you may use alge­bra or if you’re advanced, cal­cu­lus. Either way, I will know if you guess. You can use only one dec­i­mal place.

So here are the puz­zle instruc­tions. You are giv­en two posi­tion for­mu­las for a falling object. 

🧩 PUZZLE INSTRUCTIONS

You are giv­en two posi­tion for­mu­las for a falling object. Please cal­cu­late for dis­tance in meters. Each posi­tion for­mu­la will work for the puz­zle. You just need one equation

For cal­cu­lus:

s(t)=4.9t^2

For alge­bra:

v=v_0+at

Sub­mit your answer as a num­ber in meters per sec­ond. In one dec­i­mal place only! That’s very important!

Final­ly, as you cal­cu­late, Emi­ly sets a sec­ond cup down beside you.

EMILIE DU CHATELET:

You’ll need this. The night is long and so is the road to enlight­en­ment. Now, if you’ll par­don me, I have a card game to get to.

As she walks down the hall, you hear her say

If falling stones you wish to know,
What makes the pace for­ev­er grow?
Use ‘a’ in sums, but truth I tell,
It’s grav­i­ty’s hand that casts the spell.

Once you have your solu­tion, you write the val­ue in your note­book, stash it in your silk bag and walk back to your cloaked cap­sule. And with that, she grabs the pot and her cup and walks out of the room. With every step, you won­der why any­one would wear stock­ings in the snow. Back at the warm cap­sule, you sit at the helm.

The cap­sule dark­ens and the walls pulse with the voice in the capsule.

CAPSULE: One more key remains, Chrononaut. Pre­pare for your next jump. 

Chrononaut, tem­po­ral coor­di­nates are not con­firmed. I repeat, tem­po­ral coor­di­nates are not confirmed. 

Your cap­sule lands.

You look out and you see that you’re in the dock­ing bay of a large ship. Noth­ing looks famil­iar, not even the tech­nol­o­gy. Three aliens with red curly wigs, all wear­ing muumuus, are stand­ing around ancient Mayan artifacts.

Your cap­sule lights up as it alerts you.

CAPSULE: Pos­si­bly you are in the year 3025. What we do know is that you’ve been sum­moned by future archae­ol­o­gists that refer to them­selves as the Digonauts.

Okay, you weren’t expect­ing this. So you grab your notepad and pen­cil and step off the plat­form. All three red­heads look at you as though they were expect­ing you as you grasp that you have jumped five hun­dred years for­ward from your depar­ture point in 2525. You were not pre­pared for this and there were no cos­tumes in the bathroom.

One of them ges­tures you over to the artifacts.

“I’m in the future?” you ask.

MARGARET 1: Yup.

She squints at the bright room light.

MARGARET 1: Mar­garet, can you turn down those lights? Any­hoo, sor­ry to incon­ve­nience you here in the future, but I promise we’re gonna leave you with a part­ing gift. Hi, I’m Mar­garet! Lead Dig­o­naut. I like that name! I’m a Lead Digonaut!

That’s Mar­garet there in the red and the oth­er one there is Mar­garet. She’s also wear­ing red. So we’ve recov­ered a rel­ic. It’s numer­i­cal, but it’s dif­fer­ent. We need some­one bureau cer­ti­fied who was around before the knowl­edge col­lapse began.

She hands you an etched data slate. You rec­og­nize the inscrip­tion as Mayan inscrip­tion. Your neur­al HUD acti­vates. A prompt scrolls across your vision.

NEURAL HUD: Decode this viges­i­mal numer­al, ancient Mayan struc­ture. Dots are worth one each. Bars are worth five. Bot­tom row equals one’s place. Each row above equals times 20 of the row below.

You blink. A voice from your ear­piece cuts in. It’s Admin from the His­to­sci­en­ti­math­i­cal Bureau.

ADMIN

Just a reminder that if you con­vert any­thing into base ten with­out log­ging a form 17B, that’s tech­ni­cal­ly cul­tur­al ero­sion. Also, your last cof­fee ration was flagged. Caf­feine dis­tri­b­u­tion beyond the twen­ty-sev­enth cen­tu­ry is under review.

You sigh.

🧩 PUZZLE INSTRUCTIONS

You look at the screen and it reads:

MARGARET 1: We think this one is either an ancient joke or a bur­ri­to order. Save it any­way. You nev­er know when you might need it.

You pull out your notepad and write the ques­tion down, even if it was a bur­ri­to order. A Mar­garet from the oth­er end of the dock yells.

MARGARET 2: That’s the wrong num­ber!! Show them the oth­er one over there.

Mar­garet looks back at you.

MARGARET 1: Oops, sor­ry. We’re gonna scrub your mem­o­ry on that one. Here, fol­low me.

The archae­ol­o­gist ges­tures to a larg­er display.

MARGARET 1: Okay, no more stalling. Here is the one we are stuck on.

She projects a ver­ti­cal Mayan numer­al with three dis­tinct levels.

She points to a glyph on the display:

The top row reads with one dot.

The mid­dle row reads noth­ing. It’s com­plete­ly empty.

And the bot­tom row reads two bars and a dot.

You write the sec­ond answer in your notepad and show it to the red­head. You then explain to Mar­garet how it works.

YOU: Mar­garet, you see, it’s a Mayan viges­i­mal sys­tem. The dots are worth one each. Bars are five, and you read them from bot­tom to top. The bot­tom row is in the ones place, and each row above is 20 times the row below.

The dig­o­naut takes her wig off and scratch­es her head, and then puts it back on. She looks back at her cowork­ers and yells.

MARGARET 1: Hey guys, we’re over­think­ing it!

MARGARET 2: I knew it!

The Dig­o­naut hands you a cli­mate-sta­ble flask.

MARGARET 1: Thanks for your help, man. Here! It’s our own Dig­o­naut Bureau Blend, grown in hydro­pon­ic vol­canic caves, fil­tered through crushed obsid­i­an. It’s def­i­nite­ly not approved for tem­po­ral trav­el, so this part­ing gift should be kept on the down low, if you know what I mean.

You look at her and say, “I know exact­ly what you mean.” You know exact­ly where to put that cof­fee when you get back in the cap­sule. So you walk back onto your cap­sule. The door clos­es behind you as you leave the launch pad, and just like that, as though you nev­er left, you’re back home. The cap­sule shud­ders to a halt.

Home, if you can call a bureau tucked into the folds of time, home. The pres­sure equal­izes. The door hiss­es open.

You step out, blink­ing off the lin­ger­ing echo of bright cor­ri­dors, ancient libraries, and a freez­ing cold walk in the snow. You look down at your note­book, and in it are four num­bers. You stare at them.

You pause. Wait, hmm, okay, Alexan­dria, France. You flip back through your notes. Mar­garet, okay. You remem­ber the three mis­sions vivid­ly, the Library in Alexan­dria, a snow-cov­ered study in Enlight­en­ment France, and a bright cap­sule filled with Margaret’s, and yet you have four num­bers, and for some strange rea­son, it feels like your brain has been scrubbed by an inter­di­men­sion­al rub­ber eras­er. Before you leave the pod bay, a robot rolls a small cart towards you.

On it sits four satchels, each with a dif­fer­ent col­or, pur­ple, sky blue, green, and red. The robot hands you a slip of paper that reads,

NOTE: Each woman you encoun­tered today left you one clue, one item, one satchel. Unfor­tu­nate­ly, your ride back home got bumpy, and all the good­ies fell out, but we man­aged to save the cof­fee that Mar­garet gave you. We don’t know if you are aware, but that blend is ille­gal. We had to con­fis­cate that. Our sin­cer­est apolo­gies. Take a look at the gifts and the bags. If you can fig­ure out who gave you what, you will be ready for what comes next.

🧩 PUZZLE INSTRUCTIONS

You have to match each satchel to each gift. So go back through your notes, and look at all the details of each trip. Final­ly, after sift­ing through the part­ing gifts and the satchels, you gath­er them, and you walk into the Bureau’s debrief lounge, where your steam­ing cof­fee mug is waiting.

Veron­i­ca walks in and goes to her console.

VERONICA: You all right? You look like some­one hand­ed you a sand­wich and called it algebra.

You shuf­fle through the gifts. You nod slowly.

“I have four val­ues,” you say, “but I only remem­ber three mis­sions.”

Veron­i­ca taps a few keys at her con­sole and smirks.

VERONICA: Tem­po­ral drift, it hap­pens. Hon­est­ly, you’ve done bet­ter than most. Some agents come back with bunnies.

She slides a fold­er toward you.

VERONICA: Your offi­cial assign­ment was to retrieve three keys, num­bers, that, togeth­er, for in the sta­bi­liz­er sequence. But if you found more, some­thing could be wrong. Let’s take a look.

You show her the numbers.

VERONICA: Okay, there’s the first num­ber, the sec­ond num­ber, the third num­ber, a dash, and the word bur­ri­to. Bur­ri­to? Wow, were you tak­ing food orders?

“I don’t remem­ber,” you tell her.

VERONICA: There’s a fourth num­ber. All your cal­cu­la­tions look good, except for that third num­ber with the bur­ri­to nota­tion. Well, I guess your next mis­sion will be more inter­est­ing than we thought.

You look at the num­bers one last time. Still no mem­o­ry of that fourth num­ber. The only mem­o­ry that remains is the faint smell of those pre­cious vol­canic cof­fee beans.

Chrononaut, you’ve done your part for now, but the sta­bi­liz­er is not com­plete. Three num­bers were the mis­sion. Four are in your pos­ses­sion. Which ones mat­ter? Which are dis­trac­tions? And why do you have four new satchels? And what comes next? Some­thing fast is wait­ing for you, very fast.

HOLIDAY PUZZLE PART 2

Before the break, you stepped into the His­to­sci­en­ti­math­i­cal Bureau, took your first mis­sion as a Chrononaut, and trav­eled through the Library of Alexan­dria, the snowy study of Émi­lie du Châtelet, and the future arche­ol­o­gy bay run by the Digonauts.

You col­lect­ed three numer­i­cal keys, solved a Fibonac­ci sequence, cal­cu­lat­ed the veloc­i­ty of a falling stone, and decod­ed a Mayan viges­i­mal num­ber, and returned with some­thing a bit extra. You got three keys plus four satchels, and the clue: 65-bur­ri­to. Now you will gath­er three more keys, along with a few extra clues, all of which just might lead to the impos­si­ble and show you what hap­pens when sci­en­tif­ic truths turn out to be step­ping stones, when you decide to step beyond the lim­its you’ve always assumed were fixed.

When we left you, Chrononaut, you were stand­ing in the debrief lounge at the His­to­sci­en­ti­math­i­cal Bureau. Four satchels sat on a cart, pur­ple, sky blue, red, and green. Did you solve who gave you what?

These col­ors and objects will come in very use­ful as we begin the sec­ond mis­sion. You sling all four satchels across your shoul­der. Veron­i­ca meets you with the pod bay, her eyes light­ing up your cap­sule with a soft green light.

VERONICA: Well done. Now for round two, four more keys, and this time you’ll need your gad­gets. The one I gave you will come in handy for your first jump.

You step into your cap­sule, the doors seal, the walls dim.

CAPSULE: Wel­come back, Chrononaut. As usu­al, your cos­tumes are in the bath­room. Keep your notepad handy. Tem­po­ral inser­tion four, send­ing you to exo­plan­et LHS 3844B.

Your cap­sule lands on the twi­light edge of a tidal­ly locked world, one hemi­sphere eter­nal­ly scorched by its sun and the oth­er frozen in shad­ow. The atmos­phere is thin. The air is odd­ly still.

This place does­n’t spin. At the ter­mi­na­tor line where dusk nev­er fades stands a soli­tary obser­va­to­ry of gleam­ing pan­els and reflec­tive sur­faces. You run to the bath­room to find your first outfit.

It is a mer­cury coat­ed body­suit with grav­i­ty cal­i­brat­ed boots and a hel­met. On your way to leave, you look down at the satchels and grab all four. Just in case you might need one of them.

You step out­side, eyes adjust­ing to the slow pulse of dim gold and pale blue light. The watch inside one of the satchels ticks, anchor­ing your sense of time to Earth­’s frame of ref­er­ence. A door hiss­es open.

You walk into the obser­va­to­ry. It is a vast sil­very white dome. Along the walls are carv­ings, almost like the cat hiero­glyphs from the old Egypt­ian tablets.

You are met with a fas­ci­nat­ing­ly beau­ti­ful alien. It moves like mer­cury, its body mor­ph­ing from glossy obsid­i­an to glow­ing white as it tra­vers­es light and shad­ow. You can­not tell where its face is, only that it speaks with­out a sound direct­ly into your mind.

LANDLOCKED ALIEN: Chrononaut, we can­not mea­sure time in your terms. Our species evolved with­out rota­tion, but our orbit­ing satel­lite speaks only in Earth time cal­i­bra­tion. Please help us sync the signal.

A large pan­el dis­plays a number.

It says:

Dis­tance to satel­lite, 218,248,909.424 kilometers.

Trans­mis­sion method, laser pulse.

The beam ges­tures toward the con­trol pan­el and a count­down indi­ca­tor. Your mind races. How can you help them sync the sig­nal? Then you remem­ber that Veron­i­ca said the item she gave you will help. Which one did Veron­i­ca give you? She said it would come in handy.

Which bag do you open?

Now, for the trans­mis­sion method: a laser pulse. As you look around the room won­der­ing what you can use, you glance at the cat hiero­glyphs and you remem­ber Hypa­ti­a’s cat.

You know exact­ly what to use. The laser point­er. Which bag do you open?

You tell the alien, “We can use these two tools.” The alien replies.

LANDLOCKED ALIEN: Prim­i­tive beam, insuf­fi­cient for orbital transmission.

It then maneu­vers over to a halo of rotat­ing crys­talline pan­els arranged in con­cen­tric rings above a translu­cent pedestal.

LANDLOCKED ALIEN: Our pho­ton har­mo­niz­er array. You can insert your laser arti­fact here.

🧩 PUZZLE INSTRUCTIONS

So Chrononaut, here is your first chal­lenge. To prop­er­ly sync the trans­mis­sion, you must cal­cu­late how long it will take for a laser pulse to trav­el from the obser­va­to­ry to the satel­lite. You will use the dis­tance for­mu­la solv­ing for time.

D=rt

The dis­tance for­mu­la is dis­tance equals rate mul­ti­plied by time, with rate in this case being the speed of light.

When you maneu­ver things around, you find that time equals dis­tance divid­ed by speed.

t=\frac{D}{r}

The dis­tance from the land­locked plan­et to the orbit­ing satel­lite is 218,248,909.424 kilo­me­ters. And the speed of light, it is 299,792,458 meters per sec­ond squared. So you will need to con­vert kilo­me­ters to meters for this equa­tion. Your answer will be in seconds.

Write this num­ber in your note­book. It is the fourth key in your sta­bi­liz­er sequence. After you write it in your note­book, you insert Hypa­ti­a’s tool into the base.

The array begins to shim­mer. It aligns its lens­es and inter­nal prisms to ampli­fy and har­mo­nize the sim­ple beam into a focused quan­tum sta­ble sig­nal capa­ble of space trav­el. The laser’s red flick­er stretch­es, sharp­ens and becomes a blind­ing col­umn of light, nar­row, hum­ming with precision.

You punch the answer into the con­trol pan­el. Veron­i­ca’s earth cal­i­brat­ed watch ticks exact­ly as you press the sync but­ton. A thin beam of light, pure, nar­row, unwa­ver­ing, launch­es into the sky, slic­ing through the plan­et’s hazy exosphere.

It van­ish­es into the dark­ness, bound for the dis­tant satel­lite. For a moment, the plan­et is still. The mer­cury alien shifts, refract­ing like a prism under a lens flare.

It paus­es.

LANDLOCKED ALIEN: Satel­lite await­ing con­tact. Trans­mis­sion is aligned.

It does not smile. These beings have no mouths, no eyes, but a faint shim­mer puls­es across its sur­face like a silent applause. It bows with unnerv­ing precision.

The alien speaks.

LANDLOCKED ALIEN: Earth sec­onds. Now under­stood. Thank you.

The alien tilts its head, its limb now mor­ph­ing gen­tly from sol­id to translucent.

LANDLOCKED ALIEN: Safe trav­els. Chrononaut.

The cap­sule speaks in your earpiece.

CAPSULE: One addi­tion­al key acquired. Mis­sion accomplished.

You walk back to your cap­sule and take off.

CAPSULE: Buck­le up. New coor­di­nates plotted.

The audio becomes war­bled and inco­her­ent. You try to over­ride the com­mu­ni­ca­tion mod­ule to read the next des­ti­na­tion, but the screen goes black. Sud­den­ly, your cap­sule comes to a screech­ing halt and docks to a glass tube with a mov­ing con­vey­or belt.

Your com­mu­ni­ca­tion mod­ule and screens are back up. Your cap­sule speaks coherently.

CAPSULE: Chrononaut, it’s time for cof­fee. Wel­come to the Red Roam­ing Cafe inter-time­line branch.

You look up and you see a dri­ve-up cafe float­ing in space, straight out of the Jet­sons. You run to the bath­room look­ing for a cos­tume. You see two. George or Jane, pick your favorite. You step out of your cap­sule and onto the belt that deliv­ers you to your des­ti­na­tion. The doors slide open and you are in a very bright, bustling cafe in space.

The cafe is too bright for you. Then you remem­ber that you have some­thing in one of the satchels. What is it and what col­or is the satchel?

You look around, tables float in lazy ellipses. Mugs spin gen­tly, but nev­er spill. Sta­bi­lized by invis­i­ble mag­net­ic fields. A neon sign over the bar flickers.

It says,

“Serv­ing all time­lines since… we forgot.”

A wide vari­ety of aliens and his­tor­i­cal earth peo­ple are sit­ting at tables, laugh­ing and drink­ing cof­fee. One of the baris­tas turns around. She’s wear­ing the same muumuu and has a wig full of red curls.

You know that face. She’s one of the Mar­garets from the Dig­ga­naut team, just on her side hustle.

“Mar­garet!” you exclaim.

MARGARET 3: Hey, it’s you. You’re the Bureau’s favorite math nerd time trav­el­er. You want a coffee?

You nod intense­ly. You need that coffee.

She hands you a steam­ing mug.

MARGARET 3: How many cups of cof­fee have you had since you first start­ed your adventure?

You raise your eye­brows at her. You take a sip. It’s strong, a lit­tle smoky, with some­thing like cin­na­mon and starlight.

MARGARET 3: It’s good, right? It’s the blend your boss con­fis­cat­ed. Don’t wor­ry, your secret’s safe with me. Okie dok­ie, today’s spe­cial comes with a puz­zle, chem­istry fla­vored, and a side of burrito.

She winks. She snaps her fin­gers and a bur­ri­to wrapped in red foil comes fly­ing at your face. She puts her hand up and grabs it right before it touch­es your nose. She slams it down on the table.

An eight-legged, spark­ly green alien with four faces on its head yells.

CAFÉ ALIEN: Oh, wait­er, yoo hoo! Over here.

MARGARET 3: I’ll be back. My cus­tomers await.

You look down at the bur­ri­to, real­iz­ing that since you start­ed the mis­sion, you haven’t had a thing to eat. You start to open it and you smell fresh hatch chilies. It’s human food. As you peel back the foil, on the inside of the red wrap­per, in big hand­writ­ten num­bers, it says 65.

Below it, it is writ­ten,

Don’t lose this. It’s not the price, it’s a clue.  

Some num­bers you car­ry. Some num­bers car­ry you.

You pull out your comm device and take a pic­ture while you devour the bur­ri­to. The bur­ri­to has but­tery, refried black beans, chori­zo, gooey cheese, and fresh Hatch chilies, onions, and cilantro, and some­thing that you just can’t fig­ure out. This bur­ri­to is the most deli­cious bur­ri­to you’ve ever had in your entire life. It must be the Hatch chilies. Right behind your head, a white­board hov­ers in the air.

You set­tle in. You munch on your bur­ri­to while you solve the puz­zle. Puz­zles, ille­gal cof­fee, and the world’s great­est burrito.

You debate nev­er leav­ing this cafe.

On the white­board, two val­ues appear:

Light roast cof­fee: pH 6.4
Dark roast cof­fee: pH 4.9

Under­neath, a reminder:

[H^+ ]=10^{-pH}

It is an equa­tion also known as the antilog­a­rithm of the neg­a­tive pH. Basi­cal­ly, the H plus is called a hydro­gen cation. It’s also called a pro­ton, and it means the hydro­gen ion con­cen­tra­tion in moles per liter.

It can be cal­cu­lat­ed from the pH of the cof­fee using the inverse of the pH for­mu­la, which is a base 10 exponentiation.

Mar­garet floats back with her serv­ing tray.

MARGARET 3: I’m a ding-dong, I for­got the guac and chips.

She puts it on the table and holds up the cof­fee pot.

MARGARET 3: Oh yeah, hey, just a reminder, acid­i­ty in cof­fee is tied to the con­cen­tra­tion of hydro­gen ions. pH is just a way to com­press that into a nice lit­tle log­a­rith­mic scale. Small dif­fer­ences in pH can mean big dif­fer­ences in acid­i­ty. You don’t want a grumbly tum­my. Refill?

Of course, you tell her, know­ing the reper­cus­sions while trav­el­ing in a small cap­sule. She pours you anoth­er cup.

MARGARET 3: If light roast has a pH of 6.4 and dark roast has a pH of 4.9, how many times more acidic is the light roast? That is, what’s the ratio of their hydro­gen ion con­cen­tra­tions? Divide the [H⁺] con­cen­tra­tion of the dark roast by the [H⁺] con­cen­tra­tion of the light roast. One dec­i­mal place or no more cof­fee for you. She smiles and taps the for­mu­la. Use the pH for­mu­la. Don’t pan­ic. It’s just expo­nents in dis­guise. Kind of like that bur­ri­to wrap­per that is more than pack­ag­ing. It’s a prod­uct for tur­bu­lent times if you get my drift. She winks again and floats away.

🧩 PUZZLE INSTRUCTIONS

So, Chrononaut for this puz­zle. Light roast cof­fee has a pH of 6.4. Dark roast cof­fee has a pH of 4.9. You’re going to divide the hydro­gen ion con­cen­tra­tion of the dark roast by the hydro­gen ion con­cen­tra­tion of a light roast. And hydro­gen ion con­cen­tra­tion is rep­re­sent­ed as follows:

[H^+ ]=10^{-pH}

And again, it’s just expo­nents and divi­sion. So you’re going to find how many times more acidic is the light roast than the dark roast. You com­pute the ratio, round your answer to one dec­i­mal place and write it down as a number.

This val­ue is key five in your sta­bi­liz­er sequence. Mar­garet floats back over.

MARGARET 3: Don’t lose that bur­ri­to wrapper.

You ask her what’s inside the bur­ri­to while you fold the red foil and put it in your notebook.

MARGARET 3: Hon­est­ly, beans and hatched chilies from your plan­et. After taunt­ing the humans in Area 51, we took a road trip and smug­gled out a case of those chilies. But real­ly, the math is the spicy part.

Sud­den­ly, the cafe begins to shim­mer. The mugs, the white­board, Mar­garet’s curls, all stretch like taffy and snap out of sight. Your cap­sule catch­es you like a safe­ty net.

CAPSULE: Two keys col­lect­ed in this mis­sion. Check your satchels.

You look over and see four satchels, one pur­ple, one sky blue, one red, and one green. Which tool haven’t you used so far? With­in one breath, the entire cap­sule starts to shake.

The grav­i­ty loosens as you try to cal­i­brate its pull with­in the cap­sule. The ride is bumpy, and you’re not feel­ing very confident.

CAPSULE: Hold tight, Chrononaut . Coor­di­nates are unknown. Search­ing for next inser­tion point.

Stars fly past you. This has nev­er hap­pened before, and you are hop­ing that you will get out of this alive.

CAPSULE: Inser­tion point locat­ed. Brace for impact.

The cap­sule hur­tles through the time stream, spin­ning end over end. A halo of turquoise light wraps around the hull as you cling to the con­sole for dear life, some­where between cen­turies. Grav­i­ty tilts side­ways, and the cap­sule slams into some­thing solid.

The cap­sule clips the very tip of St. Paul’s Cathe­dral. A show­er of slate frag­ments scat­ter across the Lon­don rooftops as the machine skids off the tow­er, spi­rals and careens down­ward, land­ing in a mud­dy field just out­side the city. Steam hiss­es from the cracked hull.

The door wheezes open. You get thrown across the cap­sule and land in front of the door to the bath­room. You catch your breath. You check your­self. Oh, good. No bro­ken bones.

You’re just a lit­tle shook up. The cap­sule is at a tilt as you try to stand up. You ask the com­put­er, where you are.

CAPSULE: You have arrived in Lon­don, Eng­land, in the earth year 1835. By the way, the hull to this cap­sule is cracked. Tar­get Augus­ta Ada King, Count­ess of Lovelace, math­e­mati­cian, vision­ary, hero of algo­rith­mic imag­i­na­tion, and the pri­ma­ry rea­son the His­to­sci­en­ti­math­i­cal Bureau’s no unsu­per­vised access to pro­to­types waiv­er was retired after only three hours.

Sec­ondary tar­get Charles Bab­bage, inven­tor, engi­neer, con­nec­tor of griev­ances against street musi­cians, and the man who once attempt­ed to math­e­mat­i­cal­ly quan­ti­fy irri­ta­tion. Approach with cau­tion. He may attempt to recruit you to assist in reor­ga­niz­ing his workshop.

Decline if pos­si­ble. By the way, the hull to this cap­sule is cracked. Mis­sion para­me­ters, retrieve and assem­ble four miss­ing punch cards whose com­bined val­ue will advance your cur­rent objective.

Be advised that the ana­lyt­i­cal engine is in a state of par­tial func­tion­al­i­ty, par­tial inspi­ra­tion, and par­tial T‑related dam­age. Reminder, the Bureau strong­ly dis­cour­ages dis­cussing mod­ern com­put­ing con­cepts in Ada’s pres­ence. The last agent to men­tion Wi-Fi pre­cip­i­tat­ed the great algo­rithm arms race of 1852.

Pro­ceed with dis­cre­tion, admi­ra­tion, and min­i­mal col­lat­er­al math­e­mat­i­cal inno­va­tion. By the way, the hull to this cap­sule is cracked, but Charles and Ada may have some­thing that can help you.

You pry open the bath­room door and see an 1835 cos­tume com­plete with puffy sleeves and ruf­fles. You put it on and sling the four satchels, pur­ple, sky blue, green, and red, over your shoul­der and trudge toward Lon­don. Gas lamps flick­er in the gath­er­ing dust.

Horse carts rat­tle over cob­ble­stones. And inside a large work­shop on Dorset Street, two bril­liant minds are argu­ing over some­thing that appears to be a pile of wood, gears, and paper.

ADA LOVELACE: Charles, we are miss­ing four punch cards. Not one, not two, but four.

CHARLES BABBAGE: Ada, my dear, I do not mis­place cards. They migrate.

ADA LOVELACE: They are not migra­to­ry crea­tures, Charles.

You step inside quietly.

ADA LOVELACE: Hel­lo there. You look as though time has knocked you about a bit.

You reply, “it does that fre­quent­ly.”

CHARLES BABBAGE: Do you know any­thing about mis­placed com­pu­ta­tion­al artifacts?

You tell him, “I might. What exact­ly are you look­ing for?”

ADA LOVELACE: Four punch cards that must be added togeth­er. When com­bined, they cre­ate one spe­cif­ic val­ue. With­out that val­ue, the ana­lyt­i­cal engine can­not pow­er our experiment.

CHARLES BABBAGE: Or, I sus­pect, fix the Jed­lik trav­el­ing machine.

Trav­el­ing machine, that gets your atten­tion. You raise your eye­brows and say, “I’ll help.”

Ada finds the first card under a teacup, stained with a per­fect ring of earl grey. Charles dis­cov­ers the sec­ond inside a draw­er that he claims he nev­er uses. You pull the third card from between two gear cogs, and the fourth appears to be behind the engine’s brass frame. That was def­i­nite­ly not a migration.

They spread all four cards across the table.

ADA LOVELACE: These, when added, will give us the num­ber we require. We need to pow­er up a trav­el­ing machine we found so that, per­haps, it will live again.

You look at the punch cards. Each card holds sev­en columns that are num­bered from bot­tom to top, zero through nine. Each card rep­re­sents a sev­en-dig­it val­ue, a whole number.

The hole punch­es tell you what each dig­it is. Card one reads one, one, five, sev­en, eight, zero, two. So when you look at them, it reads 1,157,802.

The fol­low­ing cards are as follows.

You get the num­ber you need, and then you write it in your notebook.

ADA LOVELACE: The pow­er­ing appa­ra­tus is over here. As you can see, it is an elec­tro­mag­net­ic rotat­ing device. It pow­ers Jed­lik’s trav­el­ing device that we had found sit­ting in a ravine out in the field. How­ev­er, we can­not get it to work. We had worked some cal­cu­la­tions, but the punch cards we had, accord­ing to my friend Charles, had migrated.

She says that using air quotes while look­ing at Charles. The elec­tro­mag­net­ic rotat­ing device is con­nect­ed to the ana­lyt­i­cal machine. One by one, you feed the punch cards through the read­er of the ana­lyt­i­cal machine.

Each card slides through. The engine’s pins drop with a mechan­i­cal series of clicks. The num­ber has been added. Inside the machine, gears lock into place. A mas­sive cen­tral wheel begins to rotate.

CHARLES BABBAGE: Ah, there she goes, a flaw­less cal­cu­la­tion in progress.

A nar­row strip of paper emerges from the out­put slot. Tiny holes trac­ing a pre­cise math­e­mat­i­cal pattern.

ADA LOVELACE: Let’s punch this into pow­er up the batteries.

She punch­es it in, but noth­ing happens.

ADA LOVELACE: Fartle­ber­ries, it’s not work­ing. Got any ideas?

You think about your satchels, but noth­ing comes to mind. Then you remem­ber Mar­garet, the bur­ri­to wrap­per from the roam­ing cafe. The num­ber 65 scrib­bled on the wax paper and Mar­garet’s cryp­tic warning.

MARGARET 3: It’s a prod­uct for tur­bu­lent times if you get my drift.

You get it! Prod­uct! The pieces final­ly fac­tor togeth­er. You pull out the bur­ri­to wrap­per and unrav­el it. They look at you oddly.

You tell them, float­ing cafe, best bur­ri­to ever. You then pull out your note­book and run some cal­cu­la­tions and voila, you just found the sixth key. You write down the num­ber and then you show the num­ber to Ada.

“Here, try this,” you tell her. She man­u­al­ly types up the new num­ber into the ana­lyt­i­cal machine and the elec­tro­mag­net­ic rotat­ing device pow­ers up.

ADA LOVELACE: Yes, this is it. Let’s get this to Jed­lik’s Mir­a­cle Car­riage and get it moving.

Ada and Charles lead you to the field where the car­riage sits in a ravine. There sits a sky blue elec­tric car­riage decades ahead of its time. The exper­i­men­tal vehi­cle built by Agnos Jed­lik just sev­en years earlier.

Ányos Jedlik’s Mod­el for an Elec­tric Car (Budapest Uni­ver­si­ty of Tech­nol­o­gy and Economics)

And just 10 meters away is your par­tial­ly cloaked cap­sule with a crack across the roof. Star­ing at your cap­sule, Charles says.

CHARLES BABBAGE: That, that can­not exist.

ADA LOVELACE: Dear, dear Charles, inven­tion rarely waits for permission.

You, Ada and Charles, car­ry the elec­tro­mag­net­ic rotat­ing device over to the sky blue elec­tric car­riage. You con­nect it and wait. The entire car­riage pow­ers down.

Curi­ous, the trav­el­ing device is incom­plete. And then you remem­ber some­thing. Star­ing at the car, you then look at the match­ing sky blue satchel and you remem­ber Emi­ly telling you about dri­ving a car with the Com­man­der of the Chronofold.

You pull your final tool out of the bag. What is it?

You pull the key fob out of the blue satchel and hit the start but­ton. The elec­tric car­riage starts up and starts run­ning, get­ting faster and faster. And then it coughs, sput­ters, and then stops.

The poor machine still lacks an instruc­tion. You’re not sure what to do next. You’ve tried everything.

So you press your com­mu­ni­ca­tor and call Veronica.

VERONICA: Oh good, you’re alive. I was on a cof­fee break.

You explain to her that you’re stuck in 1835 with Ada Lovelace, Charles Bab­bage, Agnes Jed­lik’s elec­tric car, and four punch cards and a bur­ri­to wrap­per that don’t add up to enough electricity.

VERONICA: That is quite a to-do list. Here’s your prob­lem. You did­n’t fin­ish the puz­zle. You need to add all six keys, but no bur­ri­to wrapper.

She takes a sip and then looks at you with wide eyes. All six? Your eyes widen and then you remem­ber everything.

Hypa­ti­a’s num­bers, Emi­ly’s num­bers, Mar­garet’s viges­i­mal num­bers, every­thing you gath­ered in all of your jumps. You open your note­book. On the first page are your three keys from your first mis­sion. Veron­i­ca ver­i­fied all of them except for the bur­ri­to nota­tion. And on the next page are your three new keys. Key four, the time the pulse hit the satel­lite from the land­locked planet.

Key five, the acid­i­ty ratio between light and dark roast cof­fee. And key six, the total from Emi­ly and Charles’ punch cards fur­ther cal­cu­lat­ed in your note­book with the help of Mar­garet’s bur­ri­to wrap­per. So you add up all the keys and show them to Ada and Charles.

They punch it in and it works. You have all suf­fi­cient­ly pow­ered up the Jed­lik car­riage. Ada whis­pers into Charles’ ear.

ADA LOVELACE: Charles, that is one dig­it more than-

CHARLES BABBAGE: Shh, Ada. I want to see where this goes. Chrononaut, I must ques­tion, which cen­tu­ry do you tru­ly call home?

You reply. “Hon­est­ly, I ask myself the same question.”

VERONICA: Good work, every­body. Ada, Charles, can my Chrononaut  use the spare parts from our bro­ken cap­sule to cre­ate an oxy­gen safe cap­sule around Jed­lik’s car to dri­ve it back to 2525?

CHARLES BABBAGE AND ADA LOVELACE: Most def­i­nite­ly. — But of course!

VERONICA: Thank you. Chrononaut , I will meet you at the His­to­scien­tomath­i­cal Bureau.

So you fol­low Veron­i­ca’s instruc­tions and you now have a lev­i­tat­ing car with an elec­tric blue field. It does­n’t have a bath­room, but it will get you back home. You grab your satchels, your note­book, and put them in the carriage.

The sky blue car­riage ris­es in a shim­mer­ing glob­al light. You hit the key fob, acti­vat­ing the igni­tion. The bub­ble col­laps­es inward and launch­es you into the time stream.

Moments lat­er, you land back in 2525, right out­side the His­to­sci­en­ti­math­i­cal Bureau. Veron­i­ca is wait­ing with a clipboard.

VERONICA: All right, let’s see what you brought us.

For the satchels? You show her what is inside each one and who it is from.

VERONICA: Very good, Chrononaut.

You show her the numbers.

VERONICA: Excel­lent. That was the num­ber that you need­ed to pow­er up Jed­lik’s car­riage. Do you rec­og­nize any­thing inter­est­ing about that num­ber? Do you remem­ber Ada whis­per­ing to Charles? What did she say right before you left? What is that num­ber? I believe it was men­tioned on the Tidal Locked Plan­et. If you’ve done all the math cor­rect­ly, your final sta­bi­liz­er val­ue should be just a lit­tle bit faster than some­thing very famous. And what does that num­ber say about exceed­ing your own expec­ta­tions? You did it. You exceed­ed the impossible.

Remem­ber that. Now, where is the sev­enth number?

“The sev­enth?” you ask.

You’re shocked. You ask her, “what, the sev­enth number?”

VERONICA: Yes, the final num­ber of this entire mis­sion, the one that com­pletes the sequence and sta­bi­lizes the knowl­edge continuum.

You are shocked. You thought you had gath­ered all the num­bers. You failed the mis­sion and you’re not sure what to say.

VERONICA: Veron­i­ca taps your note­book. The sev­enth num­ber is the num­ber of cups of cof­fee you drank on this jour­ney. We have to track those. I told you that when you first started.

You look down at your log­book and there is one blank line left. How many cups of cof­fee did you drink on this adven­ture? Go back through your notes and write it down.

That is the final num­ber. Now that you have all of the puz­zle pieces pro­vid­ed to you in one episode, go over your notes. 

You will need to submit:

• The val­ue to the sev­en keys
• A list of what was in each col­ored satchel

And when you are fin­ished, send your work, send a screen­shot or a scan of it, as well as all the answers to hello@mathsciencehistory.com!

Again, that is hel­lo at mathsciencehistory.com. All the answers must be in on Tues­day, Decem­ber 16th at mid­night Pacif­ic time. And we will announce the win­ners on Fri­day, Decem­ber 19th on our flash­card Fri­day episode.

And if you are so brave, we would love to inter­view you and learn about your love and obses­sion with math, sci­ence and his­to­ry. So again, fin­ish the puz­zle, send us your answers and the work before Decem­ber 16th at mid­night Pacif­ic time. And we will announce the win­ners on Fri­day, Decem­ber 19th.

I hope you enjoyed this puz­zle. It is for every­body around the world, who­ev­er is lis­ten­ing to it. I will accept answers from all parts of this planet.

Be the first one to solve it cor­rect­ly. Email me your work and your answers, and you will receive a choice of Math Sci­ence His­to­ry mer­chan­dise and a $25 Ama­zon gift card. The sec­ond run­ner up, sec­ond one to get it in with all the cor­rect answers and show­ing your work will receive a Pow­ered by Curios­i­ty T‑shirt brought to you by Math! Sci­ence! History!

And the third will receive one of our lat­est Math! Sci­ence! His­to­ry! com­put­er stick­ers. Again, all answers must be in by Tues­day, Decem­ber 16th by mid­night Pacif­ic time. Win­ners will be announced on our flash­card Fri­days episode on Fri­day, Decem­ber 19th.

And until then, keep your cof­fee warm, keep your mind sharp and your coor­di­nates close. This is the His­to­sci­en­ti­math­i­cal Bureau sign­ing off.

Carpe diem!!