Perhaps puzzles aren't an American thing.
Perhaps, because we all know that mental acuity and geographic location are biconditionally related.
The second puzzle, tells you the answer...All that is required is a bit of General Knowledge.
Once again, I have no intent on attempting to throw guesses at these alleged "puzzles." I thought since you relented the answer for the first, you might do the same for the second. My mistake.
As for your puzzle......Applying basic puzzle formats, one initially doesn't need to come up with anything other than 6.....
So your answer is "6"? There's no need to separate yourself from your answer by stating, "one initially doesn't need to come up with anything other than 6..." And no, the answer is not "6." (You were close, though.) You see, I can't expect you to figure it out just from its mere presentation--not even for a "keen" puzzler like yourself. Of course, you're going to state that it's "6" based on the only reasoning you can grasp from its presentation, and that is its order. But if I keep the rules to myself, how can the answer be determined by you or anyone other than guessing at the rules? Presenting a series of numbers and making one of them a mystery doesn't necessarily make it a (number) puzzle. Now I can drag this out like you did and pretend that I'm testing your "mental acuity," but I won't. The answer is 23/4 (or 5 and 3/4.) And the rules are rather simple: the mystery number is based on applying an order of operations incorporating each of the previous five numbers. Also the mystery number is necessarily greater than five, but less than six.
(1^2 x 3)/4 +5
I couldn't expect anyone to discern this merely from looking at the series of numbers as I presented them. One would literally have to guess. And that's the folly with your number puzzle: once you declared that your series of numbers was not a sequence, you declared it to be absent of a consistent rule. Thus, it became a guessing game, whether you acknowledge it or not.