Shifting Stones

Basic Info

Shifting Stones is a game played on a 3x3 grid of tiles. There are a total of 9 tiles, each belonging to one of four tile types. Each tile has two faces, so there are a total of 8 possible faces that any given grid position could contain. The breakdown of tiles is as follows:

• 1 tile with Sun/Moon faces
• 2 tiles with Fish/Bird faces
• 3 Tiles with Horse/Boat faces
• 3 Tiles with Tree/Seed faces

Given these parameters, the total number of unique configurations possible on the grid can be calculated as follws:

9!/1!(9 - 1)! * 8!/2!(8 - 2)! * 6!/3!(6 - 3)! * 3!/3!(3 - 3)! * 2⁹ = 2,580,480

or

₉C₁ * ₈C₂ * ₆C₃ * ₃C₃ * 2⁹ = 2,580,480

The objective of the game is to match patterns given on cards to the grid. For example, a player might want to arrange the grid so that a horse is directly above a boat. On a turn, a player can discard one of their cards to move a tile either horizontally or vertically (but not diagonally), or to flip a tile. This means the total possible number on moves on a given turn is 21. A player can also skip their turn to draw two more cards, but they cannot do this two turns in a row. Players start with four cards.

Terminology

The nomenclature for the board is below. Grid convention: [a0 a1 a2] [b0 b1 b2] [c0 c1 c2] Tile convention: Sun: A1 Moon A2 Fish: B1 Bird: B2 Horse: C1 Boat: C2 Seed: D1 Tree: D2

Additionally, we have several concepts that are used in the implementation of the program.

• Success State: A board position that corresponds to the card, such that the card can be played with no more movements.
• Point value is a measure of how many moves, and thus how many discards is needed to complete a card. Each flip or movement increases by one point. Exceeding three points means a card is nonviable and should be treated as discard fodder.
• Point sum is the measure of the total sum of points needed to achieve a success state given a card and board.