![]() Hence a final position with only one peg cannot be reached, since that would require that one of these numbers is one (the position of the peg, one is odd), while the other two numbers are zero, hence even. Hence after an even number of moves all these three numbers are even, and after an odd number of moves all these three numbers are odd. After every move the number of covered A positions increases or decreases by one, and the same for the number of covered B positions and the number of covered C positions. Initially with only the central position free, the number of covered A positions is 12, the number of covered B positions is 12, and also the number of covered C positions is 12. Divide the positions of the board into A, B and C positions as follows: This is easily seen as follows, by an argument from Hans Zantema. There is no solution to the European board with the initial hole centrally located, if only orthogonal moves are permitted. On the English board the equivalent alternative games are to start with a hole and end with a peg at the same position. This mirror image notation is used, amongst other reasons, since on the European board, one set of alternative games is to start with a hole at some position and to end with a single peg in its mirrored position. There are many different solutions to the standard problem, and one notation used to describe them assigns letters to the holes: On an English board, the first three moves might be: Thus valid moves in each of the four orthogonal directions are: A blue ¤ is the hole the current peg moved from a red * is the final position of that peg, a red o is the hole of the peg that was jumped and removed. indicates a peg in a hole, * emboldened indicates the peg to be moved, and o indicates an empty hole. ![]() The objective is, making valid moves, to empty the entire board except for a solitary peg in the central hole.Ī man playing triangular peg solitaire at a Cracker Barrel restaurant.Ī valid move is to jump a peg orthogonally over an adjacent peg into a hole two positions away and then to remove the jumped peg. The standard game fills the entire board with pegs except for the central hole. This is the first known reference to the game in print. The August 1697 edition of the French literary magazine Mercure galant contains a description of the board, rules and sample problems. The first evidence of the game can be traced back to the court of Louis XIV, and the specific date of 1697, with an engraving made ten years later by Claude Auguste Berey of Anne de Rohan-Chabot, Princess of Soubise, with the puzzle by her side. It is also called Brainvita in India, where sets are sold commercially under this name. The game is known as solitaire in Britain and as peg solitaire in the US where 'solitaire' is now the common name for patience. Some sets use marbles in a board with indentations. Peg solitaire, Solo Noble or simply Solitaire is a board game for one player involving movement of pegs on a board with holes. INITIAL-STATE), problem, limit) function RECURSIVE-DLS(node, problem, limit) returns a solution, or failure/cutoff if problem.GOAL-TEST(node.STATE) then return SOLUTION(node) else if limit = 0 then return cutoff else cutoff-occurred? - false for each action in problem.ACTIONS(node.STATE) do child - CHILD-NODE( problem, node, action) result - RECURSIVE-DLS(child, problem, limit - 1) if result = cutoff then cutoff_occurred? - true else if result + failure then return result if cutoff_occurred? then return cutoff else return failure Figure 3.17 A recursive implementation of depth-limited tree search.The Princess of Soubise playing solitaire, 1697 You must create classes for the playing board, the successor function and the goal test, and make your classes work with the search code from the text.įunction DEPTH-LIMITED-SEARCH( problem, limit) returns a solution, or failure/cutoff return RECURSIVE-DLS(MAKE-NODE(problem. ![]() Program Depth First Search on this problem. Jumps are permitted horizontally or vertically, but not diagonally. A piece can be removed by jumping an adjacent piece over it into an empty hole. The goal is to remove all the pieces except one, which should be in the center. In the picture above, the hole in the center is empty and the remaining holes contain pegs. Transcribed image text: Peg Solitaire is a game consisting of a playing board with 33 holes together with 32 pegs.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |