- Limited mobility due to lack of space
- Limited mobility due to function
- Limited mobility due to lack of time
Usually the term limited mobility is associated with immobility due to lack of space solely. The
trapped piece and the mated king are examples of lack of space.
Lasker added function as a cause of immobility. If you loose a piece when you move a defender, you cannot really move that defender, albeit it is allowed by the rules. The defender has limited mobility due to its function.
I extended the term immobility with limited mobility due to lack of time. This means that all duplo attacks fall under this description. If you must save two pieces but you have only time to save one, the other piece remains on the board as if it is frozen.
This augmented immobility as I defined it, comprises almost every possible technique you can throw at your opponent. All 30 or so tactical themes, and all 30 or so types of mate. I hypothesize that you can't find a combination that is not based on this augmented immobility. Or maybe you can, but at least the bulk of the problems at CT has this augmented immobility at its very core.
There is of course a reason for that. In a balanced chess game, there are always several answers possible to any move. To any attacking move. A combination is by definition not balanced. A combination works, due to the fact that the options of your opponent are limited, one way or another. These limitations are always based on augmented immobility.
This means, that for a combination, you must identify the sitting ducks. Flying ducks have to much options to circumvent an attack. I have analyzed dozens of positions of CT lately, and sofar I haven't been able to falsify this hypothesis.