1. Procedural Puzzle Challenge Generation in Fujisan 富士山
Dr. Mark Goadrich – Hendrix College
James Droscha – Glastyn Games

2. FujisaN: A Solitaire Puzzle Game

3. Fujisan Elements
2 Rows x 12 Columns of spaces with values between 0 and 5 inclusive
4 Shinto Priests start off the board on either side
GOAL: Move Priests one at a time until all four are at the summit.
24 Values
1 2×2 Summit
10 Steps
24 Spaces
4 Priests

4. Fujisan Movement Rules
A Priest may move onto a space if that space’s value
matches the number of unoccupied spaces the Priest
must move in a straight line, left or right, to get there
(including the destination space itself, but not
including the Priest’s starting space).
Occupied spaces (containing intervening Priests)
are not counted when determining the distance from
a Priest to a given space.
A Priest may pass over the summit as part of a move.
A Priest that lands on the mountain’s summit can no
longer move left or right, but may still move
freely up or down within the column.
A Priest may move freely up and down between the
two spaces of any given step of the mountain.

5. How To make Fujisan Challenges?
The solver must use the pieces of the game to setup their own challenges.
Is the setup process easy for the solver?
Can all such challenges be solved?
How difficult are the created challenges?

6. Solitaire Puzzles and Procedural Content Generation

7. Solitaire Puzzle Games
Fifteen Puzzle, Tipover, Peg Solitaire, Sokoban, Monument Valley

8. Procedural Content Generation
Offline Constructed Deterministic Necessary
Online Generate-and-Test Randomized Optional
Making Challenges for Solitare Puzzle Games is like making Levels for Video Game Puzzle Games

9. RUSH HOUR
Offline Constructed Deterministic Necessary
Randomized

10. Klondike Solitaire Online Generate-and-Test Randomized Optional
Necessary?

11. 5 setup Algorithms

12. Piecepack Game System
24 square tiles, indexed on the obverse in four suits (suns, moons, crowns, and arms) of six values each (null, ace, 2, 3, 4, and 5) and divided on the reverse into a 2×2 space grid.
24 round coins, each sized to fit comfortably into one space on a tile, marked on the obverse with one of the six values and on the reverse with one of the four suits.
4 cubic dice, one per suit, each side marked with one of the six values.
4 pawns, one per suit, each sized to fit comfortably into one space on a tile.

13. 1. Pure Random TEDIOUS ≈ 1018 Challenges
Take one die from the piecepack. For each space, roll the die and place a coin that matches the number rolled on the space.
≈ 1018 Challenges
0 – 24 of each value

14. 2. Any Coin BETTER ≈ 1015 Challenges
Shuffle the 24 coins face-down. For each space on the board, randomly select one coin and place it face-up on this space.
≈ 1015 Challenges
4 of each value

15. 3. Piecepack rules OK ≈ 1010 Challenges
Shuffle the 24 coins face-down, and separate into four groups based on their suit. Then repeatedly place two coins on the two right-most available spaces, choosing from each of the suits in turn (sun, moon, crown, arms).
≈ 1010 Challenges
4 of each value
Step values cannot be identical

16. Alternate Pieces? 20 Engraved Tiles 15 Dominoes
double-five mirrored configuration
minus all-0 tile
15 Dominoes
double-five configuration
minus tiles with identical value

17. 4. Engraved Tiles EASY ≈ 107 Challenges
Shuffle the tiles face-down. Then assemble the mountain using face- up tiles, using six for the bottom row, five for the next row, then four, then three, and finally two.
≈ 107 Challenges
0-7 of each value
Step values cannot be identical
Step values only repeated at summit

18. 5. Dominoes EASY ≈ 105 Challenges
Shuffle the dominoes face-down. Place 12 of these dominoes face-up in a row to create the mountain.
≈ 105 Challenges
2-5 of each value
Step values cannot be identical
Step values cannot be repeated

19. Results

20. Fujisan Simulator C# implementation 1000 Challenges per Setup
(1,13) -> (1,8)  
(1,8) -> (1,3)  
(1,3) -> (0,3)  
(0,3) -> (0,1)
(0,0) -> (0,2)  
(0,1) -> (1,1)  
C# implementation
5 PCG Setups
A* Solver
1000 Challenges per Setup
10 Trials of 100 Challenges

21. Remaining Questions Can all such challenges be solved?
How difficult are the created challenges?

22. Solvability Recorded percent of solvable challenges for each strategy
t-test results
Random < Any Coin
Any Coin < piecepack
piecepack < Domino

23. Difficulty
Random
Any Coin
Recorded minimum length solution for each solvable challenge
Follows Poisson distribution
Kruskal-Wallis H-test
p-value = 1.93 x 10−8
Engraved Tiles is the culprit!
Missing 0 values?
piecepack
Engraved
Dominoes

24. Understanding The Results
Good Fujisan challenges have
Non-obvious moves (need 0 values)
Well-connected steps (non-identical step values)
Well-distributed values (non-repeated step values)

25. Future Work Formalizing Easy of Physical Setup
Shuffling and Sorting different for computers and humans
Enriching Difficulty Metric
Are all moves equal?
What about branching factor?
Can PCG for Solitaire Puzzles be Online and Constructive?
Must avoid being tedious
Must avoid giving away the solution
Dominoes lack mountain aesthetic?