For example, consider a checkerboard with the single squares at 2 opposite corners removed. Can the board be exactly covered with a set of rectangular tiles each of which covers 2 squares? If the problem is represented naively, discovering the answer depends on searching through all the possible arrangements of tiles. The simple representational device of noticing that the ``mutilated'' board has 32 black squares and 30 white ones, and that each tile covers one square of each colour, however, makes it trivially obvious that the task is impossible.
Modeling is also key in scheduling. For example, by representing the precedence of tasks to be scheduled (what comes before what), rather than the start times for tasks, the size of the search space can be reduced dramatically without loss of generality or functionality.