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Here is a short identification puzzle inspired by a road trip across the U.S.

There are four sets of clues, each identifying a state.
Please identify each state and what they have in common/why they specifically are significant.
A clue or set of clues may have multiple possible answers, but only one combination forms a complete answer.

a)

  • Not one of the original states
  • image is on its right
  • image could fit within it
  • The last letter is the same as the first letter
  • mystery flag
  • Imports false charity into the Keystone State

b)

  • Near image
  • Nearly enter image description here
  • Associated with cars and also pollution
  • Quite low density

c)

  • Potatoes, say
  • Imports crude petroleum into the Mount Rushmore State
  • Has a recognizable shape
  • Contains part of the mind (Freudian)

d)

  • 10,000 lakes, generally
  • Has more freedom than (c)
  • Forms part of Lake Superior
  • images
  • Also contains a part of the mind

Hint:

Little or no knowledge is required to solve this puzzle. There are a few viable break-in points (in my opinion); solving any will quickly lead you to the answer.

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These four states are...

the four states of matter! From OP: matter is a synonym for "significance", as per the title

The first state is...

Plasma

Explanation:

Plasma isn't one of the "original" states of matter (solid, liquid, and gas). Massachusetts is on its right (plasMA), and Louisiana could fit within it (pLAsma). The last letter (in "plasma") is the same as the first (in the alphabet). Hidden from Arizona's flag is a star, and stars are made of plasma. "Imports false charity into the Keystone State" is almost a cryptic clue, where "charity" = "alms": P(LASM)*A.

The second state is...

Gas

Explanation:

Montana's abbreviation is "MT", and fuel gauges have "empty" on them from OP: gas is mostly "empty" space. "GAs" is nearly Georgia (GA). Gas is used to fuel cars, pollution is commonly gaseous, and gas is quite low density.

The third state is...

Solid

Explanation:

Potatoes are an example of a solid. "Imports crude petroleum into the Mount Rushmore State" is another almost-cryptic-clue, where "petroleum" = "oil": S(OLI)*D. Solids can hold their shape (and thus have recognizable shapes) and contain part of the mind, according to Freud: solID.

The fourth state is...

Liquid

Explanation:

Lakes are generally liquid, and can change their shape more easily than solids. You can have liquid assets and river banks, but deserts and brick houses are usually dry? From OP: "Stocks and cash/cash accounts are considered liquid assets; land and buildings are not." Liquids also contain part of the mind, according to Freud: liquID.

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    $\begingroup$ Oh, well done :) Now that I read your answer I understand that I had made a massive assumption throughout, which the OP has been very careful never to state... I'd even solved some of the more cryptic clues and rejected the answers because they didn't fit my preconception. Great work seeing through the deception! $\endgroup$
    – Stiv
    Aug 19 '21 at 15:19
  • $\begingroup$ @Stiv Why thank you! :D When I first saw the puzzle, I thought that there would be something tricky afoot; it just took me coming back to it later for the pieces to click $\endgroup$
    – samm82
    Aug 19 '21 at 15:23
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    $\begingroup$ Great work! Some notes on intention: (rot13: Tnf vgfrys vf zbfgyl rzcgl. Fgbpxf naq pnfu/pnfu nppbhagf ner pbafvqrerq yvdhvq nffrgf; ynaq naq ohvyqvatf ner abg. Nyfb gur gvgyr 'Fgngrf bs Fvtavsvpnapr' vf n flabalz sbe lbhe nafjre) $\endgroup$
    – Amoz
    Aug 19 '21 at 18:26
  • $\begingroup$ @Amoz Thanks for the clarification; I added it to my answer (I was almost on the right track for the rot13(yvdhvq nffrgf) part! XD) Great misdirection throughout, and it was a fun solve once I figured out what was happening! $\endgroup$
    – samm82
    Aug 19 '21 at 20:25

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