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Take a good look at the numbers below and tell me

Which Geographical Region is represented by the blank circle and why?

enter image description here

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    $\begingroup$ This should mentioned that it is U.S. specific. $\endgroup$ – jimjim Jul 3 at 4:12
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    $\begingroup$ @jimjim I think if you mention that then you are giving a rather large hint which isn't required. Part of the puzzle is making that association yourself, as opposed to being told it. Otherwise you might as well throw in the other connection too... $\endgroup$ – musefan Jul 3 at 9:53
  • $\begingroup$ @jimjim Thanks for your comment. I just gelt that that particular hint would have made the puzzle too easy. $\endgroup$ – DEEM Jul 3 at 17:51
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I think the geographical is:

Florida as this has state abbreviation FL, and the symbol for Flerovium is Fl atomic nbr 114.

The pattern is:

Use 1A to Z26 to convert the two numbers in the circles to two letters, which are US states and chemical symbols. Then two circles point to another if the sum of their atomic numbers equals the pointee.

The question shows these:

(1 12) Al [atomic nbr 13] + (1 18) Ar [atomic nbr 18] → (7 1) Ga [atomic nbr 31]
(7 1) Ga [atomic nbr 31] + (14 4) Nd [atomic nbr 60] → (16 1) Pa [atomic nbr 91]
(16 1) Pa [atomic nbr 91] + (14 5) Ne [atomic nbr 10] → (13 4) Md [atomic no 101]
(13 4) Md [atomic no 101] + (1 12) Al [atomic nbr 13] → (7 12) Fl [atomic nbr 114]

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I'm pretty sure it's

Florida.

The numbers encode, somewhat amazingly,

two-letter combinations that are abbreviations for both US states and chemical elements

and to combine two of them along the arrows, you just

add up the atomic numbers,

which, by some bizarre cosmic coincidence, seems to produce another suitable member in the set quite often. Wow.

(The kids require attention, so I'll type in the rest of the details soon.)


EDIT: Here are the promised details (for some extremely dubious values of "soon", and in picture format instead of typing, because @Tom already did the typing bit, and I thought the logic might be somewhat easier to follow this way.):

enter image description here

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    $\begingroup$ Bizarre cosmic coincidence is the fact that you and @Tom came up with the same answer within seconds of each other!! $\endgroup$ – DEEM Jul 1 at 13:50
  • $\begingroup$ @DEEM : this is a U.S. Specific puzzle, otherwise Florence or something similar should also be accepted. $\endgroup$ – jimjim Jul 3 at 4:13

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