> you compare it to guessing the number 12,859,155. I took that to mean the rules are very hard (take a lot of tries) to guess correctly.

The puzzles in The Witness can be obvious from a certain perspective and so then if you have that perspective there's only one answer, why can't everybody see that. But if you lack that perspective, or worse, have slightly different perspective which you have falsely believed to be correct, you struggle.

If I know every US sports team's nickname then a Connections solution which hinges on knowing New York's team names seems obvious. If I didn't even know who the "Yankees" are then I'm going to find that particular connection hard to understand. Likewise if you know Lead's atomic symbol is Pb then you're going to more easily see that the letters PB might be related to a clue you had previously thought was about the verb "lead" not the noun.