Peg solitaire

Peg solitaire is a single-player board game in which pegs jump over adjacent pegs into empty holes, removing each jumped peg. The usual goal is to finish with one peg.

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Peg solitaire jump: A move in peg solitaire that jumps one peg over an adjacent peg into an empty hole, removing the jumped peg. Every ordinary move follows this rule, which determines the game's possible states.
English peg solitaire: The cross-shaped peg-solitaire variant commonly played on a 33-hole board. This is the best-known form associated with the game's early European history.
Combinatorial game theory: The mathematical study of games with defined states, moves, and outcomes. Peg solitaire is a finite move system that can be analyzed with game-theoretic tools.
Artificial intelligence planning: The computational task of finding action sequences that achieve specified goals. A peg-solitaire solution is a plan from an initial board to a target.
Peg solitaire board: A layout of holes that defines where pegs can be placed and which jumps are possible. Board geometry determines which sequences can reach a one-peg finish.
French peg solitaire: A peg-solitaire variant played on a 37-hole board with a distinctive pattern of diagonal moves. Its larger board illustrates how the game developed beyond the English layout.
Graph theory: The study of graphs, mathematical structures made of vertices connected by edges. A board can be represented by holes and their spatial relations.
Depth-first search: A graph-search algorithm that explores one path as far as possible before backtracking. It can enumerate jump sequences while using little memory.
Peg solitaire solution: A sequence of legal jumps that reaches a specified peg-solitaire goal from a given starting position. A solution is a complete path through the game's changing positions.
European board games: Board games developed or widely played in Europe across different historical periods. Peg solitaire entered European accounts as a distinctive single-player pastime.