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Show HN: Jumping Julia Maze

jumpingjuliamaze.onrender.com

35 pointsthathoo15 comments

This is inspired by Julia Robinson Mathematics Festival. https://jrmf.org/

The wording isn't good. The number does not indicate how many jumps you need to make. It indicates how far you need to jump.

Otherwise fun!

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!

Knowing that a typical maze will have branching paths at the beginning, but necessarily one good path at the end, I find it easier to start from the goal and work my way backward.

It seems to make a server request when Generating a new maze. Making the maze working fully Client side should be doable..

Just for amusement, tried:

https://jumpingjuliamaze.onrender.com/?width=7&height=3

and ended up with a 3 wide 7 high table... but with a projected Goal square at 7 wide 3 high?

This is great. Simple to get, not too simple to solve. One I will share with my kids, plus now introduced to Julia Robinson festival. Thanks for sharing.

Are these always solvable? The handful of 4x4's I've had don't seem to be.

With arbitrary generation rules they are surely not. This is a counter example on 4x4:

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

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

This seems to be able to be understood as a reachability graph problem of some sort perhaps.

Edit: formatting

I did about 10 4x4s and 6x6s and they were all solvable.

Worth noting, since it was absent in the rules, that it is unnecessary to touch all of the squares.

Seems like I'm too late and it got hugged to death? Page is not loading for me.

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.

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.

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