I've made a couple of puzzle games for jams before this (LD42) entry - LD40, LD36, LD27, GMCJam13, GMCJam9 etc.

Generally - this means creating a bunch of puzzle levels in a very short span of time, and you don't particularly have time to put much thought into pacing the puzzles.

I generally follow a rule of having the last 2-3 levels include every mechanic in the puzzle, while the rest of the levels introduce new puzzle mechanics spaced evenly. Just to pace things out, and not overload the player with information. My first 2-3 levels almost always are extremely simple solutions, to make sure the player gets your base mechanic (plus, it helps you pad the number of levels ;) ).

• When making the puzzle, I generally start by placing the goal and the player first (if there's a clear goal - if not, by deciding the end condition).
• A second step normally would be to decide what I want out of that level - do I want to reinforce an idea to the player? Do I want them to figure out a certain mechanic can be used in a special way? (For example, the shown level is explaining the various ways teleporters can be used, through gameplay. I force the player to use a teleporter multiple times - emphasizing that they're reuseable).
• Now I imagine a path to that end goal - which almost always never stays the same by the end of designing.
• I start designing in reverse. Now that I want them to follow this set of directions, what do I do to make players follow this?
• I start placing pieces which will help towards that goal.

That's it! If you want to see some of that method in action, you could try out our game - Mindblocked!