Show HN: Jumping Julia Maze

[thathoo]

https://jumpingjuliamaze.onrender.com

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

[phkahler]

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!

[Ntrails]

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?

[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!

[khebbie]

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

[pierrebai]

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.

[monkeydust]

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.

[panki27]

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

[wingmanjd]

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

[Atiscant → wingmanjd]

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 |

Or

  | 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

[CrazyStat → wingmanjd]

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

[jumpoddly → wingmanjd]

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

[kjrfghslkdjfl]

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

[Atiscant → kjrfghslkdjfl]

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 → kjrfghslkdjfl]

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

[Atiscant → 420official]

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.