Four Shinto Priests have traveled from their various prefectures in pilgrimage to the top of Mount Fuji. You must find pathways for them to move up and down the mountain until they can all achieve the peak. Often, this will require you to guide them into positions from which they can assist each other.
James Droscha is best known as the designer of the piecepack game system, and one of his early piecepack games was a solitaire called Fujisan. He and Mark Goadrich then adapted it for dominoes and pawns in a paper on using entangled components in solitaire games.
I was excited to learn about the domino version, because I had written software to find harder than average layouts of the piecepack version, and I was collecting Domino games.
This week, I'll be posting three new problems here on Puzzling.SE, getting more challenging each time. Don't worry if you don't have dominoes, you can print out the diagram. Here's the layout for today's problem, see the rules below.
Set up the dominoes to match the starting position above.
For a random starting position, remove all dominoes with the number six and all doubles from a standard set of double-six dominoes. Shuffle the remaining 15 dominoes face down, then place twelve face-up dominoes side by side. Leave the three remaining dominoes face down, and use them to lift up the two middle dominoes as the peak of Mount Fuji.
Place a Priest (pawn) beside each number at both ends of the mountain.
Moving a Priest
- A Priest may move onto a space if the number matches the number of unoccupied spaces the Priest must move in a straight line to get there (including the destination space itself, but not including the Priest's starting space). For example, a Priest may move onto a space with the number 4 if there are 3 unoccupied spaces between it and the Priest.
- Occupied spaces (containing intervening Priests) are not counted when determining if a Priest may move onto a particular space. For example, a Priest may move onto a space with the number 2 if there are 3 occupied spaces and one unoccupied space between it and the Priest.
- A Priest may move freely between the two spaces on a domino. This is the only manner in which a Priest may move onto a blank space.
- Once a Priest lands on the peak of the mountain, he will refuse to leave it, but he can move back and forth (in the same domino) or to and fro (between the two dominoes). Clarification: A Priest may pass over the peak dominoes as part of a move.
- A Priest must enter the mountain from his own starting row; that is, he cannot move back and forth while he remains on the ground.
The Priests will be content when they all reach the top of the mountain.
Post your solution as an answer with each move labeled for pawn A, B, C, or D, the direction, and the number of steps. If someone else has posted an answer, see if you can find one with fewer moves.