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Show HN: Jumping Julia Maze

jumpingjuliamaze.onrender.com

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Re: Show HN: Jumping Julia Maze

#14

Post by Atiscant »

420official wrote: post #12
kjrfghslkdjfl wrote: post #3

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

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

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.

Re: Show HN: Jumping Julia Maze

#15

Post by Atiscant »

kjrfghslkdjfl wrote: post #3

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

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.

Re: Show HN: Jumping Julia Maze

#16

Post by pierrec »

I love the concept. I was left wanting more because larger puzzles are apparently not more difficult, they just seem to have a lot of solutions. But can we make them more difficult? Just in case anyone else wants more of a challenge... I hand-wrote a 10x10 that should be harder to crack:

    1  2  1  2  2  3  1  1  2  2
    3  2  3  3  3  3  3  3  3  3
    3  3  3  3  3  3  3  3  3  3
    2  1  2  2  3  2  1  1  3  1
    2  1  3  3  1  3  3  1  3  1
    3  3  1  3  3  3  3  3  3  3
    2  3  2  2  2  2  1  2  2  3
    3  3  3  3  1  3  3  1  3  2
    1  3  2  3  3  3  3  3  3  3
    2  1  3  3  2  2  2  2  1  F
Unless I made a mistake, the simplest solution is not easy to find. Obviously I was thinking about an algorithm to create harder "Jumping Julia" puzzles. Definitely doable, but for now I'll leave it at that!
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