Puzzles are essentially generated by creating many random boards until a certain number of them satisfy a few basic conditions. Then, a score is given to each board, and the board with the highest score is ultimately chosen. The settings "strict," "fast," and "balanced" change the amount of valid boards required for the algorithm to proceed to the second step. What this means is that with a stricter setting, you'll see fewer edge cases where the board itself is acceptable but is given a low score (such as a board where all solutions come from the same set of tiles), but the wait time between rounds might be longer depending on how powerful your computer is.
Also, the last round on the timeline is a tiebreaker, which is why it's a diamond instead of a circle. If there is no tie at the end of the penultimate round, there's no need to go on to the tiebreaker! The tiebreaker board has only one solution, only tied players participate, and answering incorrectly will lock you out from the rest of the round. Note that if you're only playing with 1 player, you'll never reach the tiebreaker.
