This is a special maze called the Jumping Julia:

A small 5x5 Jumping Julia maze.

As with other mazes, there is a start and a finish, and you must find a path from one end to the other. However, movement through this maze works differently. Each tile has a number on it to indicate how far you must jump when moving away from it, and your entire jump must happen in only one direction. Only the four cardinal directions are legal (no diagonal movement allowed). There are no wraparounds, and if you cannot jump the required number of spaces without going past an edge, then that direction is not legal for that tile.

What is the shortest path to get from the start to the finish?

While solving this puzzle, I quickly picked up on a few interesting concepts:

  • The puzzle is unidirectional, i.e. just because I can move from tile A to tile B, that does not guarantee that I can return from tile B to tile A. In fact, I can only do that when tile A and tile B both have the same number on them.
  • It's possible to be trapped inside an inescapable maze. In the image below, there are four tiles with the number 3 on them that are all 3 spaces away from each other. Once you've landed on any of those tiles, you cannot escape from them.
  • Spoiler: I found the easiest way to solve this puzzle was by working backwards. This is because the number of paths to explore grew too numerous when exploring in the forwards direction, but the paths could be pruned off when exploring in the reverse direction.
It is possible to be trapped on the selected four tiles, because there is no way to escape.

Once you've solved the smaller puzzle, here's a bigger one:

A large 7x7 Jumping Julia maze.