The article talks about a 2-dimensional grid which starts at (0,0) (bottom right) and extends infinitely to the right and the top, so all (x,y) for non-negative integers x,y exist. But x or y negative does not exist. Given a list of possible jumps e.g. (+1,+10) or (-20,+13), and a target destination, e.g. (700,1). Does there exist a series of valid jumps that takes you from (0,0) to (700,1) without ever going off grid (i.e. into negative territory)?
This problem might or might not be NP-Harder. However, now extend the problem to higher dimensional grids. At some number of dimensions, the problem becomes definitely NP-Harder (i.e. NP-hard, decidable, but not in NP)
Which number of dimensions, though? Is there an effective bound? Otherwise it is hard to suggest the problem as an example.
The number of dimensions is one of the variables in the problem.