Soitaire

Problem Description

Solitaire is a single player game played on a 7x7 board with 2x2 corners omitted. Each position is either full (containing a peg / marble) or empty. With 'O' representing full positions and '.' representing an empty position, a possible board configuration is:

• OO

• OO

O.OOOOO
OOO.OOO
OOOOOOO

• O.O

• OOO

Each turn the player must jump a peg over an existing peg and removed the 'jumped' peg. For example, numbering the board from the top left, moving peg (4,2) down would give the following board configuration:

• OO

• .O

O.O.OOO
OOOOOOO
OOOOOOO

• O.O

• OOO

The task is, given an initial board configuration, find a sequence of the given number of moves.

Input Format

Thirty two facts giving the initial board configuration, each of which is either:

full(X,Y).

or

empty(X,Y).

indicating that position (X,Y) is either full or empty.

A number of time facts, giving the number of moves that must be found. These are given as a range of consecutive, ascending integers, starting at 1.

Output Format

The input facts plus a number of move facts equal to the number of time facts. Each move fact is of the form:

move(T,D,X,Y).

indicating that to get to time step T from time step T-1 (the initial conditions are regarded to be time step 0), the peg in position (X,Y) is moved in direction D (up, down, left or right).

Calibration

Generally the fewer pegs remaining on the board, the harder it is to make a move. Thus instances starting with a full or a nearly full board and conduct 27-31 moves are the most difficult.

Comment

This problem took part in the Second ASP Competition and was proposed by Martin Brain.

Author(s)

• Yuliya Lierler
  • University of Kentucky, USA
• Marcello Balduccini
  • Kodak Research Labs, USA