"Ah, Sequence, there you are," said the Chief Investigator as Sergeant Sequence entered the briefing room. "Your man Patrick Terne is on the move again, and we need your help to track him down."

"Where's he been this time?" asked the Sergeant, cradling his morning coffee.

"All over - a lot of time in Asia, then Europe, Russia, and last we heard he's in Virginia."

"The US?"

"No, South Africa, actually - but we've had a tip-off that he's heading for the US next, specifically one of the fifty state capitals... We're just not sure which. Cast your eye over this..."

Sergeant Sequence took a look at the list of locations where his nemesis had been spotted and took a sip of his coffee...

  1. Shanghai, China
  2. Beijing, China
  3. Bukittinggi, Indonesia
  4. Kiev, Ukraine
  5. Yerevan, Armenia
  6. Reykjavik, Iceland
  7. Novosibirsk, Russia
  8. Virginia, South Africa
  9. Unknown - one of the 50 US state capitals...

After a couple of seconds, Sequence laughed. "I know exactly where he's going, sir." He wrote a city on the whiteboard. The CI smiled.

"I can always count on you!" he said, warmly.

TASK: Identify the pattern behind the sequence of cities and the US state capital that Terne will be visiting next.

  • $\begingroup$ I don't think it changes the puzzle, but it looks like Kiev is now spelled Kyiv. $\endgroup$
    – SteveV
    Aug 29 '21 at 21:17
  • $\begingroup$ @SteveV That was actually a deliberate choice on my part. If you see the correct answer to the question, hopefully you'll see that this way there's a little more obfuscation :) (But yes, these days there are political reasons to spell it Kyiv...) $\endgroup$
    – Stiv
    Aug 29 '21 at 21:27
  • $\begingroup$ Great puzzle! What is the last city that he can ever visit? $\endgroup$ Aug 31 '21 at 5:06
  • 1
    $\begingroup$ @DmitryKamenetsky Thanks :) It's fairly straightforward to get to 12, via e.g. rot13(fsnK, jhKV and KVaorV), but 13 is a struggle without going INCREDIBLY obscure. And anything from 19 onwards has an exxtra level of difficulty! I stuck at a list of 9 because the city to be sought here can be defined really nicely without being ridiculously obscure. $\endgroup$
    – Stiv
    Aug 31 '21 at 6:44

The city Terne will visit next is:


The break-in:

There are a lot of repeated letters in most of the cities, and quite a few ABA patterns, but KIEV eliminates any "double letter" or "letter patterns" from consideration...there's just not enough there there.

But then...there are a lot of repeated I's. And there are quite a few V's, too. That makes you think...Roman numerals. Add the title: "you can COUNT on Sgt. Sequence", and you're there.

The data:

Remove all of the letters that are not Roman digits (I,V,X,L,C,D,M) from each city and you get:

1. shanghaI → I
2. beIjIng → II
3. bukIttInggI → III
4. kIeV → IV
5. yereVan → V
6. reykjaVIk → VI
7. noVosIbIrsk → VII
8. VIrgInIa → VIII

The answer:

So the next city Terne will visit must be a US capital with IX=9 in it. Full disclosure: I was literally in PHOENIX last week on vacation, and I still had to look it up, because I'm old and dumb. But either way it made sense to look at a list to see that it was the only one. Anyway, the only US capital with an X in it is in fact PHOENIX and it transforms via phoenIX → IX.


If we miss Terne in the States, he'll be in Luxembourg next! OR NOT...the M, the M! Must be sfaX!

  • 1
    $\begingroup$ Very nice Jeremy, well done :) 'Old and dumb', my foot! $\endgroup$
    – Stiv
    Aug 29 '21 at 21:30
  • $\begingroup$ Can't tell you how long it took to find a suitable option for stop#3... $\endgroup$
    – Stiv
    Aug 29 '21 at 21:30
  • $\begingroup$ @Stiv Given how weird it ended up being I imagine it was tough, but it doesn't seem like that should be the tough one. But I can't tell you how stupid I felt to be looking at the list of capitals, and realizing "oh, I was just there...derp". Really fun puzzle, and you did a great job disguising the mechanism! $\endgroup$ Aug 29 '21 at 22:42
  • $\begingroup$ You'd think, but so many also had C or L (or one of the others)... Just to point out a couple of Easter Eggs laid in this puzzle (very small ones, practically unnoticeable this time... rot13(Gur nooerivngvba bs Puvrs Vairfgvtngbe gb PV lvryqf n Ebzna ahzreny (101) naq Frdhrapr'f hfr bs "V xabj RKnpgyl..." pbaprnyf n uvqqra VK.) Nothing major, just enjoyed putting them in there :) $\endgroup$
    – Stiv
    Aug 30 '21 at 10:54
  • 1
    $\begingroup$ @Stiv: For what it's worth, I noticed the "Chief Inspectoring 101" ref -- or at least wondered about it. $\endgroup$
    – M Oehm
    Aug 30 '21 at 11:34

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