All good points and beautifully expressed.
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Resolved: "Long distance move" should be one of the Tactics Themes selections.
A general problem in solving a chess puzzle is that it's easy to just focus on one part of the board. Then it is easy to miss moving a piece six squares away or more.
Recently I played chess with real people in the world and in one game I failed to move my king out of check because I was oblivious to that area of the board. It was 5 minute chess so I only felt dumb for 5 days.
Then in some tactics puzzles it seems like a glorious solution if the first move has the queen moving six squares. In hiking, it would be like six miles.
And I sort of remember one wonderful puzzle where the solution had three different rook moves from one corner to another.
Thank you, chess friends.
(Moving a piece back towards where it came from is also difficult to see, but that is a different Theme)