Action puzzles is my term for puzzles that take place in the middle of action. Furthermore, they're puzzles that take doing something active to solve the puzzle (i.e., achieve the desired result). They're not puzzles that merely require thinking. They aren't appropriate for every game, but for the right game, they can be quite involving.
For instance, maybe you're fighting in the American Civil War and it takes a long time to reload your rifle. A better way to fight might be shoot an enemy, pick up his gun and use it to shoot another enemy, pick up his gun and use it….
One of my favorite action puzzles was in Star Trek Voyager: Elite Force. You're on an alien ship and some very frightening aliens come through the portals. If you destroy the portals, beautiful little creatures that look like fireflies swarm around the portals and repair them. It's annoying as hell, because you can never keep the portals damaged for long.
Down a long corridor is a transporter you need in order to get out of there. But it's broken. Suddenly it occurs to you how to fix it: You go back to the main area and start shooting objects along the corridor. This lures the "fireflies" to follow you, for they're drawn to broken machinery or devices.
They repair each object you damage in turn, until they finally "see" the broken transporter. They swarm around it and repair it, allowing you to escape.
There are many types of action puzzles. I'd love to hear a description of your favorites. If you have some you'd like to share, go to www.freemangames.com and click on "Participate."
Not only was this a wonderful action puzzle, but it was also a great plot twist in that these "fireflies," which previously you hated, turn out to be the only solution to your problem of transporting out of this dangerous environment. Brilliant.
One big danger in action puzzles is making them so difficult that the player can't figure them out. The result can be a tremendous amount of frustration.