Knossos Games - Hexagonal Ordering

For the math themed September/October issue of Imagine, I decided to make another hexagonal ordering puzzle. Below is the problem space. You'll notice that there are many similar paths that can be taken in this puzzle. In the right section of the puzzle, it is necessary to use (8,9,3), otherwise you will be stuck on the second pass. On the left side of the puzzle, it's easy to jump directly to (7,4) from multiple hexagons, but doing so will also cause you to be stuck on the second pass.