Prodigious Plentiful Perplexing Puzzles

The fastest way I've found so far is by doing The Spiral Weave with the story Strange disturbances. You don't have to kill anything, and a run takes 10 seconds.

Simply start the delve on any difficulty and walk a few steps forwards. Check for the box "Pipe-Filled Chest" at the back of the room, near the right brazier. If it's there, solve it, then right click your portrait to leave the delve. You spawn at the door, so you can instantly start a new delve.

If it's not there, right click your portrait, leave the delve and try again.

In Spiral Weave on the story "From the weaver with love" there is a CRATE on the right side. You have to kill eight easy trash mobs to get to the puzzle.
The Puzzle is the one click Pipe game.

Not sure of the point of this game?

Just to add to this as well, Underkeep on "Runaway Evolution" is really quick too. The box will be in the very first room, you'll see it as soon as you enter the delve.

If it is not there, then just leave delve, and enter again.