Ravikumar, “Peg-solitaire, string rewriting systems and finite automata”, Theoretical Computer Science, 2004. “Generalized Hi-Q is NP-Complete”, IEICE TRANSACTIONS, 1990. A related interactive tool is available here.
#Peg solitaire board game how to#
shows how to obtain board configurations corresponding to the 10 Arabic numerals and the 26 letters of the ISO basic Latin alphabet in both the uppercase and lowercase variant starting from a rectangular $7 \times 5$ board that is completely filled by pegs except for the center hole. The proof can also be adapted to the case in which no final configuration is mandated and the goal is that of fidning a solution consisitng of at least some number $k$ of valid moves. provides a zero-knowledge proof of knowledge for solutions of peg solitaire. proves the NP-completeness of the Peg Solitaire Reachability problem. However, for rectangular boards of fixed (constant) height, deciding whether a given configuration can be transformed into a single peg is polynomial-time solvable, since solvable instances form a regular language. Have only one peg (hence, the goal is cleaning the entire board). proves the NP-completeness of those peg solitaire puzzles in which the final configuration is required to Peg Solitaire Reachability is a puzzle in which, given an initial configuration of pegs on a finite board, one is asked toĭetermine whether there exists a sequence of Peg-Solitaire moves that allows any peg to be placed in a given target position. Peg Duotaire is a two-player variant of Peg Solitaire in which two players alternatively make a peg move and the winner is the last player to move. Solitaire Army is based on the game mechanics of Peg Solitaire. The initial configuration into the final one. Third one, then we can remove the two pegs and place a new one on the thirdĪ puzzle of peg solitaire is defined by an initial and a finalĬonfiguration, and consists of finding a sequence of moves that transforms The first and the second nodes are occupied by pegs and there is no peg on the The initial configuration of pegs evolves by performing one of the following moves (the jumps):įor each triple of horizontally or vertically adjacent nodes, if In Peg Solitaire (also known as Hi-Q), we have a grid graph (the board) on each of whose nodes (the holes) there may be at most one peg. Given an initial and a final configuration of pegs on a board, find a sequence of peg-solitaire moves that transforms the initial configuration into the final one.
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