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This puzzle is part of the Monthly Topic Challenge #12: mobile-friendly puzzles.


For each of the following sequences, identify the three missing terms (marked by '???'):

  1. Nitrogen, Fluorine, Argon, Phosphorus, Yttrium, Uranium, Uranium, Gold, ???, ???, ???, Carbon.

  2. Niue, Brazil, ???, Puerto Rico, Morocco, Niger, Libya, ???, ???, Tonga, Norway, Germany.

  3. ???, East London, Manchester, Preston, Manchester, ???, Liverpool, Guildford, Sheffield, Canterbury, ???, Derby.

The three sequences are related. (Please only post an answer once you can explain all three together...)

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  • $\begingroup$ (I ummed and ahhed over whether this constitutes 'mobile-friendly' but on balance I believe it does, as the subject matters fall within commonly used spheres of knowledge on Puzzling, and I believe the question can be answered quite comfortably on a mobile phone without feeling the need to rush for a laptop or something bigger...) $\endgroup$
    – Stiv
    Jul 4, 2023 at 14:42

1 Answer 1

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So each of the three given lists has the property that:

it can be encoded with a mono-/digraph in context. The first list consists of chemical elements, which can be encoded with their atomic symbols. The second is a list of countries, and can be encoded with the ISO 3166-1 Alpha-2 standard. The third is a list of metropolitan areas in the United Kingdom, and can be encoded with their postcode areas.

Placing the encoded lists next to each other, we get:

1. N - NU - ???
2. F - BR - E
3. AR - ??? - M
4. P - PR - PR
5. Y - MA - M
6. U - NE - ???
7. U - LY - L
8. AU - ??? - GU
9. ??? - ??? - S
10. ??? - TO - CT
11. ??? - NO - ???
12. C - DE - DE

The answer:

Each of the given codes is the first instance of a code that appears in the English month that corresponds to the position in the list. So for example, the first atomic symbol appearing in JANUARY is N, as none of J, JA, A, or AN is a valid atomic symbol. Similarly, neither of JA nor AN is a (current) ISO 3166 symbol (though both have been used historically...sneaky!), but NU is. Hence the complete lists are:
1. Nitrogen, Fluorine, Argon, Phosphorus, Yttrium, Uranium, Uranium, Gold, Sulfur, Oxygen, Nitrogen, Carbon.
2. Niue, Brazil, Morocco, Puerto Rico, Morocco, Niger, Libya, Australia, Sweden, Tonga, Norway, Germany.
3. North London, East London, Manchester, Preston, Manchester, North London, Liverpool, Guildford, Sheffield, Canterbury, North London, Derby.

A final note:

The title "This won't work with US states" is appropriate because JUNE, for example, contains no US postal code abbreviation. Except that as Stiv pointed out, it does (NE - Nebraska). But July really doesn't contain a US postal abbreviation. I think...

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    $\begingroup$ All perfectly correct, good work - except (cough) Nebraska...! ;) $\endgroup$
    – Stiv
    Jul 4, 2023 at 15:12
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    $\begingroup$ @Stiv Well, THAT'S embarrassing :-) I'll go fix! $\endgroup$ Jul 4, 2023 at 15:13
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    $\begingroup$ (cough) Lyisiana... (joke) Looks good to me! Well done. On reflection, I reckon this question is probably on the cusp of mobile-friendly (since its intricacies take a bit more than 'a few lines of text' to explain), but it's a simple premise at heart - hopefully still enough of a challenge! $\endgroup$
    – Stiv
    Jul 4, 2023 at 15:50
  • $\begingroup$ @Stiv Perhaps wrongly I did solve it on my computer, not a mobile device. But because of that I probably wrote more explanation than was strictly needed... Anyway, I thought the puzzle was really clever...thanks! $\endgroup$ Jul 4, 2023 at 21:13
  • $\begingroup$ Ha, still a legitimate solve :) Nothing in the rules says it has to be solved on a phone, just that it should be solvable on a phone :) And I'm glad you enjoyed it! $\endgroup$
    – Stiv
    Jul 4, 2023 at 21:23

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