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It was 2am and Sergeant Sequence had been called in to Headquarters urgently. The second he stepped through the door a file was pressed into his hands by the Chief Investigator, who began to talk extremely fast while steering him towards a side-corridor.

“Patrick Terne is at it again. Triple poisoning this time – arsenic – huge quantities of it; he wasn’t taking any chances. Fled London, hopped about all over the world, but the trail’s gone cold. We traced him through eleven different countries but he’s gone totally off grid. Of course, we suspect there is some kind of pattern to his movements – there always is – but we can’t spot it… We need your eye on this case – you know him well; if anyone can get into Terne’s mind, you can…”

It was true – Sergeant Sequence had come up against Terne on several occasions before, and each time he had been able to determine the method to his madness. Staring down at the list in his hands, Sequence pondered the countries written there…

  1. Vietnam
  2. Finland
  3. Portugal
  4. Germany
  5. Colombia
  6. Moldova
  7. Tonga
  8. Canada
  9. Tuvalu
  10. India
  11. Kenya

But then where…?!

After just two minutes of thought, something clicked. “He’s still in Kenya,” he said. “Send your best team out there.”

“How can you be so sure?” the Chief Investigator asked, an eyebrow raised.

“I know how this guy's mind works,” Sequence replied. “And trust me – if he’s done what I think he has it would have been impossible to make a twelfth move.”

TASK: Identify the pattern behind the sequence “Vietnam, Finland, Portugal, Germany, Colombia, Moldova, Tonga, Canada, Tuvalu, India, Kenya” and explain why it ends there.

Hint:

The sequence relies on TWO pieces of knowledge in combination.

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  • $\begingroup$ V unir gnxra nyy gur pbhagevrf naq ercynprq gurz jvgu gurve fhz (nppbeqvat gb rnpu pbhagel'f nycunorgf' vaqvprf naq nsgre nqqvat H+00<fhz sbe rnpu pbhagel> guvf vf jung V tbg: nUE0pUZ6Yl9jLKA0MJWcov5wo20iImN1IJIlHGH= Nz V ba gur evtug genpx? $\endgroup$ – John Brookfields Jun 29 at 8:09
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    $\begingroup$ I spent far too long trying to find significance in the name before I got it :) $\endgroup$ – Mohirl Jun 29 at 10:37
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    $\begingroup$ I've been trying do do something with the capital cities as I can't see anything else that they all have in common apart from all having one. Not come up with anything yet but maybe it gives someone smarter than me an idea. $\endgroup$ – ElPedro Jun 30 at 13:38
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    $\begingroup$ Another great one Stiv...thanks! $\endgroup$ – Jeremy Dover Jul 1 at 11:38
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    $\begingroup$ @JeremyDover Feel free, as long as you don't kill them off! :) (Although if I reuse the characters I am more likely to do a prequel anyway...) $\endgroup$ – Stiv Jul 1 at 12:27
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First take the capital cities of the countries in order

Hanoi
Helsinki
Lisbon
Berlin
Bogota
Chisinau
Nuku'alofa
Ottawa
Funafuti
New Delhi
Nairobi

Now notice that

The beginning of each capital city gives the chemical symbols for the first $11$ elements of the periodic table in order.

Hanoi
Helsinki
Lisbon
Berlin
Bogota
Chisinau
Nuku'alofa
Ottawa
Funafuti
New Delhi
Nairobi

So the next country he would have to visit would have to have

Its capital city begin with Mg which does not exist.

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    $\begingroup$ Weirdly, I knew it would be you who ended up solving this! Well done - this is exactly the right logic :) (Note one typo in the bold text of your second block though...) $\endgroup$ – Stiv Jul 1 at 9:30
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    $\begingroup$ @Stiv Ah, yes, thank you, got over excited. Great puzzle! $\endgroup$ – hexomino Jul 1 at 9:32

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