Draughts
Draughts or checkers is a group of abstract strategy board games between two players played on a 10×10 board, which involve diagonal moves of uniform pieces and mandatory captures by jumping over the enemy's pieces. Checkers is played by two people, on opposite sides of a playing board, alternating moves. One player has dark pieces, and the other has light pieces. The player with the dark pieces makes the first move. Pieces move diagonally and pieces of the opponent are captured by jumping over them. The playable surface consists only of the dark squares. A piece may only move into an unoccupied square. Capturing is mandatory. A piece that is captured is removed from the board. The player who has no pieces left or cannot move anymore has lost the game. Uncrowned pieces ("men") move one step diagonally forwards and capture other pieces by making two steps in the same direction, jumping over the opponent's piece on the intermediate square. Multiple opposing pieces may be captured in a single turn provided this is done by successive jumps made by a single piece; these jumps do not need to be in the same direction but may zigzag. When men reach the crown head or kings row (the farthest row forward), they become kings, and acquire additional powers including the ability to move backwards (and capture backwards, which they cannot already do so). King's only advantage over a man is the ability to move and capture backwards as well as forwards. Notice that captured pieces are removed from the board only after capturing is finished. Thus sometimes the captured but not yet removed piece obliges a king to stop after capturing at a given field where he in turn will be captured by the adversary.
Chinese checkers
Chinese checkers is a board game that can be played by two to six people. The objective of the game is to place one's pieces in the corner opposite their starting position of a pitted 6-pointed star by single moves or jumps over other pieces.
Standard jumps can have multiple hops, but each hop must be directly adjacent. Each player puts his or her own colored marbles on one corner of the star and attempts to relocate them all to the opposite corner. Players take turns moving one marble, either a single step or a chain of one or more hops. A step consists of moving a marble to an adjacent unoccupied space in any of the six directions. In the diagram at right, Green might move the topmost marble one space down and to the left. A hop consists of jumping over a single adjacent marble, either one's own or an opponent's, to an unoccupied space directly opposite. In the diagram at right, Red might advance the indicated marble by a chain of three hops in a single move. It is not mandatory to advance the marble by as many hops as is possible in the chain. In some situations a player may choose to stop the move part way through the chain to impede the opponent's progress or to align their marbles for future moves.
Reversi
Reversi and Othello are names for an abstract strategy board game which involves play by two parties on an eight-by-eight square grid with pieces that have two distinct sides. Pieces typically appear coin-like, but with a light and a dark face, each side representing one player. The object of the game is to make your pieces constitute a majority of the pieces on the board at the end of the game, by turning over as many of your opponent's pieces as possible.
Each of the two sides corresponds to one player; they are referred to here as light and dark after the sides of Othello pieces, but "heads" and "tails" would identify them equally as well, so long as each marker has sufficiently distinctive sides. The game begins with four markers placed in a square in the middle of the grid, two facing light-up, two pieces with the dark side up. The dark player makes the first move. Dark must place a piece with the dark side up on the board, in such a position that there exists at least one straight (horizontal, vertical, or diagonal) line between the new piece and another dark piece, with one or more contiguous light pieces between them. In the below situation, dark has the following options indicated by "ghost" pieces. After placing the piece, dark turns over (flips, captures) all light pieces lying on a straight line between the new piece and any anchoring dark pieces. All reversed pieces now show the dark side, and dark can use them in later moves -- unless light has reversed them back in the meantime. If dark decided to put a piece in the topmost location (all choices are strategically equivalent at this time), one piece gets turned over, so that the board appears thus:
Now light plays. This player operates under the same rules, with the roles reversed: light lays down a light piece, causing one or more dark pieces to flip. Possibilities at this time appear thus (indicated by "ghosts"):
Light takes the bottom left option and reverses one piece: Players take alternate turns. If one player cannot make a valid move, play passes back to the other player. When neither player can move, the game ends. This occurs when the grid has filled up, or when one player has no more pieces on the board, or when neither player can legally place a piece in any of the remaining squares. The player with more pieces on the board at the end wins.
Gomoku
Gomoku is an ancient game for two players, often referred to as an advanced version of Tic-Tac-Toe. The object is to get five pieces in a row on a game board of (potentially) unlimited size. Players will alternate turns. Gomoku has been popular in the Orient for centuries
Connect Four
Connect Four (also known as Plot Four, Four In A Row, and Four In A Line) is a two-player board game in which the players take turns in dropping alternating colored discs into a seven-column, six-row vertically-suspended grid. The object of the game is to connect four singly-colored discs in a row -- vertically, horizontally, or diagonally -- before your opponent can do likewise.
Peg solitaire
Peg Solitaire is a board game for one player involving movement of pegs on a board with holes. The standard game fills the entire board with pegs except for the central hole. The objective is, making valid moves, to empty the entire board except for a solitary peg in the central hole. A 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. In the diagrams which follow, * is used to indicate a peg (in a hole) and · indicates an empty hole. Thus valid moves in each of the four orthogonal directions are:
* * · · * * * * · · * * -> -> -> · · * * · · · · * * · · Jump to right Jump to left
Jump down
->
Jump up
Three alternative moves:
* * * * * * * * * * * * *
* * * · * * *
* * * * * * * * * * * * *
* * * * * * * * * * * * *
* · · * * * *
* * * * * * * * * * * * *
* * * · · * * * * * * * *
* · * * * * *
* * * * * * * * * * * * *
* * * · · * * * * * * * *
* * · · * * *
* * * * * * * * * * * * *
Sudoku
Sudoku is a logic-based number placement puzzle. The objective is to fill a 9×9 grid so that each column, each row, and each of the nine 3×3 boxes (also called blocks or regions) contains the digits from 1 to 9, only one time each (that is, exclusively). The puzzle setter provides a partially completed grid.
Fifteen puzzle
A solved 15-puzzle It is a Sliding Puzzle that consists of a grid of numbered squares with one square missing, and the labels on the squares jumbled up. If the grid is 4×4, the puzzle is called the 15-puzzle or 16-puzzle. In this game 15 of the 16 squares of a 4×4 frame are filled with numbered sliding pieces, leaving one space in which to slide one piece at a time. The goal of the puzzle is to un-jumble the squares by only making moves which slide squares into the empty space, in turn revealing another empty space in the position of the moved piece.
N Queens
The N-queens puzzle is the problem of putting n chess queens on an n×n chessboard such that none of them is able to capture any other using the standard chess queen's moves. This means it is as if all the queens are different colors. The queens must be placed in such a way that no two queens would be able to attack each other. Thus, a solution requires that no two queens share the same row, column, or diagonal.
Tower of Hanoi
The Tower of Hanoi is a mathematical game or puzzle. It consists of three pegs, and a number of disks of different sizes which can slide onto any peg. The puzzle starts with the disks neatly stacked in order of size on one peg, the smallest at the top, thus making a conical shape. The objective of the puzzle is to move the entire stack to another peg, obeying the following rules:
Only one disk may be moved at a time. Each move consists of taking the upper disk from one of the pegs and sliding it onto another peg, on top of the other disks that may already be present on that peg. No disk may be placed on top of a smaller disk.
PS: You are to find the optimal solution from an arbitrary initial configuration.