Well, I could not come up with a good example, a deliberate attempt :)
Simulating/Modelling variant of Treasure Hunt where next place/state is revealed by a combination of the clue from previous two places. Ofcourse, I have to make the place as a shared resource - only one process can access a place/state at a time.
Now if two processes participate in this game starting from different places/points(first two places assigned randomly) - then the situation described in the problem can easily arrive - deadly deadlock! And it can not be avoided by simple numbering.