[kjrfghslkdjfl]

Better challenge: generate these puzzles in a way to have a unique solution.

[Atiscant]

Or for the mathematically inclined: How many n x n puzzles with unique solutions exists for a given size n?

n=1 is trivial, and n=2 it small enough to enumerate with 3^4 = 81 solutions, but many of them being degenerate (no solutions), but already n=3 is pretty bad with ~20.000 possible puzzles. I do not see an obvious path to compose solutions either and make use of some kind of structural induction.

[420official]

I highly doubt it's possible to have a single solution in a puzzle like this at any size

[Atiscant]

At least it is possible to force a single solution (discounting backtraces which is always possible) in 4x4:

  | 2 | 3 | 3 | 3 | 
  | 3 | 3 | 3 | 3 | 
  | 3 | 3 | 3 | 1 | 
  | 3 | 3 | 3 | G | 

I'm fairly sure the only solution here is 2 down to 3 right to 1 to goal. You can of course then use this to generate a couple of more by changing all the numbers that are impossible to reach.