# PSE Advent Calendar 2022 (Day 4): Letters to Father Christmas (Sgt. Sequence Fan-Fic)

This puzzle is part of the Puzzling Stack Exchange Advent Calendar 2022. The accepted answer to this question will be awarded a bounty worth 100 reputation.

< Previous DoorNext Door >

"Good evening, Chief Inspector. Pat Terne again?"

"Yes. We should have been on this one a long time ago, but the Royal Mail just handed over the evidence this afternoon."

"The Royal Mail?"

"It's diabolical, Sequence...there's no other word for it. Terne compromised one of the workers who handles the letters to Father Christmas."

"That dirty..."

"I know, Sequence. But we are going to need a Christmas miracle to crack this code. I hate how Terne telegraphs his moves, but we still keep missing him!"

"What do we have?"

"Eight letters to Father Christmas. We only found them because the accomplice was on holiday when the last one came in. A holiday he never came back from."

"How was the last one detected?"

"It arrived in the office on July 4. It's pretty unusual to receive letters to Father Christmas halfway through the year."

"Technically it's a bit more than halfway. July 4th was the 185th day of the..."

"Moving on...on top of that, it was from Turkey."

"And the others?"

"Found in the accomplice's desk, along with a notepad of scribbled sequences of numbers, mostly scratched out."

"What were the contents?"

"Nothing. Zip. Nil. The envelopes were all empty, even the last one we received. Just eight envelopes."

"Well, let me see the envelopes."

Sgt. Sequence looked over the envelopes for a few minutes, then returned to his desk and after a few minutes of searching the Internet, he returned.

"It's Terne alright sir, and this may be one of his boldest capers yet. Cancel the team's holidays...we're going to be busy foiling a robbery."

Based on the envelopes below that Sgt. Sequence inspected, can you determine where and when Terne plans to strike?

#### Solver Notes

The letters below are sorted alphabetically by origin country. This may or may not be significant to the puzzle solution. Many thanks to Stiv for again allowing me to borrow his characters!
• ROT13(V guvax V'ir svtherq bhg jura, ohg abg jurer. Ubjrire, guerr guvatf ner vagrerfgvat gb zr: 1) Gur snpg gung rirel nqqerff juvpu rnpu znvy pbzrf sebz rkvfgf va erny yvsr. 2) Gur ahzore bs fgnzcf ba rnpu rairybcr, juvpu V srry vf hfrshy sbe yrggre fryrpgvba. 3) V gevrq gnxvat gur mvc/cbfgny pbqrf bs rnpu nqqerff (fvapr V fhfcrpg gung jung Puvrs Vafcrpgbe fnvq, "Mvc", pyhrf gung), naq nyy cbfgny pbqrf, rkprcg sbe gung bs gur nqqerff va Ghexrl, ner pbzcbfrq bayl bs barf naq mrebrf.)
– oAlt
Dec 5, 2022 at 11:19
• ROT13(Sbe gubfr cbfgny pbqrf V gevrq pbairegvat gurz sebz ovanel gb qrpvzny gura gb yrggref ivn n-bar-m-gjragl-fvk, ohg Hehthnl naq Zrkvpb'f nqqerffrf obgu unir bar-bar-mreb-mreb-mreb nf gurve cbfgny pbqr, naq gung pbairegf gb 24 juvpu pbairegf gb K, naq gung vfa'g cebzvfvat fvapr gurer'f bar K gbb znal. Fb gurer'f fbzrguvat ryfr tbvat ba urer gung V qba'g frr lrg...)
– oAlt
Dec 5, 2022 at 11:20
• @oAlt You are EXTREMELY close. You have produced rot13(frdhraprf bs 5 ovanel qvtvgf. Creuncf gurer vf nabgure rapbqvat, sbe juvpu gurer zvtug or n fhogyr ersrerapr va gur synibe grkg, gung pna trg lbh ubzr.) Dec 5, 2022 at 12:06

Sergeant Sequence found out that

Patrick Terne will rob the bank Barclays, headquartered in London, at December 26, 2022, right after Christmas Day!

I will first talk about the time when Terne's crime will be committed, since I found it before the place.

Each envelope has a date (presumably when the accomplice sent the envelope), so it makes sense to order the envelopes by the dates. (Here a few dates may need to be translated. In my case I don't know any Lithuanian or Turkish, or any other languages related to them, so I had to translate "kovas" and "haziran".)

After putting the envelopes in chronological order, I saw that the first letters of the first names spelled out something: Lyes, Oscar, Oliver, Karolina, Olga, Elisa, Ignacio, Serkan --> LOOKOEIS, which with a space says LOOK OEIS. This, together with the tag, nudged me to find a sequence of numbers somewhere within the envelopes. I didn't know where to look at first, until I tried converting the dates into numbers. For example, January 1 is the 1st day of a non-leap year, and December 31 is the 365th. (This applies to the envelopes since 2022 is a non-leap year.) I was motivated to do this because Sequence did exactly this as well (it says in the puzzle that he found out that "July 4th was the 185th day of the [year]").

Sure enough, I found a pattern:
Feb 5 - 36th
Feb 9 - 40th
Feb 14 - 45th
Mar 1 - 60th
Mar 13 - 72nd
Mar 31 - 90th
Apr 30 - 120th
Jun 29 - 180th

At this point I should have recognized that this was a sequence of positive divisors of 360 in increasing order. Unfortunately, at the time of solving, that did not occur to me and I still went to OEIS to figure that out. Anyway, the next number in the sequence would be 360 itself, and we convert this back to a date: December 26 is the 360th day of 2022.

Now, the place where Terne will strike:

I searched the addresses, and noticed that all of them exist in real life, but I didn't know how to extract information from them. However, I remembered that the Chief Inspector said "Zip"... which could clue zip codes? And it makes sense to think about that, since we are dealing with mail after all. So then I was finding the zip/postal codes of each address.

After much searching, I found each addresses' corresponding zip codes (although I will only put the countries rather than the addresses for brevity):
Algeria - 10011*
Uruguay - 11000
United States - 01010
Lithuania - 01110
Slovakia - 01001
Mexico - 11000
Costa Rica - 10101
Turkey - 10100**

All zip codes without footnotes were confirmed by Google Maps and the World Postal Code website.
* Confirmed by World Postal Code, though not on the map but it was the first result on the database.
** Confirmed by World Postal Code, but only by searching "turkey 10100" rather than the full address. (It also says that the zip code is for Altieylul Balikesir only, without including "2 Kavalli Sokak".)
(As it turns out, OP also used World Postal Code (more details in his first comment below).)

Now, I tried converting the numbers from binary to decimal, then doing A1Z26, but it yielded nothing promising. I also tried the Bacon cipher but that wasn't fruitful either. But then I remembered that the Chief Inspector said that "Terne telegraphs his moves". So I thought, maybe we have to use a code related to telegraphs then?

I saw two on Wikipedia: the Baudot code and the ITA2 code. It seemed that the former wasn't the right code to use, so I tried the latter. When the ITA2 code is used, one gets the following letters:

Algeria - 10011 - B
Uruguay - 11000 - A
United States - 01010 - R
Lithuania - 01110 - C
Slovakia - 01001 - L
Mexico - 11000 - A
Costa Rica - 10101 - Y
Turkey - 10100 - S

Was "Barclays" a city? A province? I had no idea at first, until I searched it... and I saw that Barclays is a British bank which is quite significant (more about Barclays in the link at the start of this answer). No wonder Terne is itching to commit a crime or two there! I hope Sergeant Sequence and his team will be able to stop him in time...

My thoughts:

I found the date first. Then I was stuck on the puzzle for a good while. At first, I tried letter selection (for each envelope, taking the nth letter in one line of the sender's address, where n is the number of stamps on the envelope) but I could never make it work no matter which lines I chose. I also did a few other things which didn't yield anything.

I eventually ruled letter selection out since I saw that all addresses were real: there would be no reason to use just letter selection if that were the case. I thought that I had to do something else (or something bigger) which utilized the fact that all addresses were real. At first, I tried looking at the establishments and streets in the immediate vicinities of the addresses on Google Maps to see if there was anything suspicious that I could use, but I abandoned this method after a while. Then some time later I finally realized that zip codes were the way to go.

As can be noticed from my observations about Algeria and Turkey, I back-solved on those ones. In reality, I didn't use World Postal Code at first; I used Google Maps and Wikipedia instead. As a result, I had found "EARCLAYD" rather than "BARCLAYS". After searching the former, results for the latter came up and so I figured that the latter had to be the intended answer. Thus I started to use World Postal Code to figure out what the intended zip codes were.

• Ah, well done for seeing this through to the end - I got much of the way but couldn't get Algeria and Turkey to work out in Step 2 and hadn't yet worked out what to do with those codes anyway. Nice job :)
– Stiv
Dec 5, 2022 at 14:51
• Thanks :D (I did have trouble with Algeria and Turkey as well though, so I wish to know how OP searched for the codes.)
– oAlt
Dec 5, 2022 at 14:55
• Correct in all particulars. Am working now so I can't comment at length, but will do so this afternoon. Dec 5, 2022 at 14:58
• Re: the codes: rot13(Gur orfg erfbhepr V sbhaq jnf jbeyqcbfgnypbqr.pbz. Gur znc trbybpngvba trgf zbfg guvatf, naq gur qngnonfr pregnvayl fubjf gur znva pnaqvqngrf. V jnf ubcvat gung trggvat fbzr bs gur boivbhf barf jbhyq thvqr gur fbyire gb gur "ovanel" pbqrf sbe gur zber bofpher.) Dec 5, 2022 at 17:04
• You got almost all of my intended "clues" as well. The one that is not mentioned is rot13(Frdhrapr pbairegf Whyl 4 vagb n ahzore...qvq gung fcrpvsvpnyyl nf na vaqvpngbe.) But all in all, a fantastic job! Dec 5, 2022 at 17:05