Download Combinatorial Games Instructions

Pentago
The game is played on a 6×6 board divided into four 3×3 sub-boards (or
quadrants). Taking turns, the two players place a marble of their color
(either black or white) onto an unoccupied space on the board, and then
rotate one of the sub-boards by 90 degrees either clockwise or anticlockwise. A player wins by getting five of their marbles in a vertical,
horizontal or diagonal row (either before or after the sub-board rotation
in their move). If all 36 spaces on the board are occupied without a row
of five being formed then the game is a draw.
Pentago
The game is played on a 6×6 board divided into four 3×3 sub-boards (or
quadrants). Taking turns, the two players place a marble of their color
(either black or white) onto an unoccupied space on the board, and then
rotate one of the sub-boards by 90 degrees either clockwise or anticlockwise. A player wins by getting five of their marbles in a vertical,
horizontal or diagonal row (either before or after the sub-board rotation
in their move). If all 36 spaces on the board are occupied without a row
of five being formed then the game is a draw.
Hex
Each player has an allocated color, conventionally Red and Blue or
White and Black. Players take turns placing a stone of their color on a
single cell within the overall playing board. The goal for each player is
to form a connected path of their own stones linking the opposing sides
of the board marked by their colors, before their opponent connects his
or her sides in a similar fashion. The first player to complete his or her
connection wins the game. The four corner hexagons each belong to
both adjacent sides. Since the first player to move in Hex has a distinct
advantage, the pie rule is generally implemented for fairness. This rule
allows the second player to choose whether to switch positions with the
first player after the first player makes the first move.
Hex
Each player has an allocated color, conventionally Red and Blue or
White and Black. Players take turns placing a stone of their color on a
single cell within the overall playing board. The goal for each player is
to form a connected path of their own stones linking the opposing sides
of the board marked by their colors, before their opponent connects his
or her sides in a similar fashion. The first player to complete his or her
connection wins the game. The four corner hexagons each belong to
both adjacent sides. Since the first player to move in Hex has a distinct
advantage, the pie rule is generally implemented for fairness. This rule
allows the second player to choose whether to switch positions with the
first player after the first player makes the first move.
The SOS Game.
The board consists of a row of n squares, initially empty. Players take
turns selecting an empty square and writing either an S or an O in it. The
player who first succeeds in completing SOS in consecutive squares
wins the game. If the whole board gets filled up without an SOS
appearing consecutively anywhere, the game is a draw.
The SOS Game.
The board consists of a row of n squares, initially empty. Players take
turns selecting an empty square and writing either an S or an O in it. The
player who first succeeds in completing SOS in consecutive squares
wins the game. If the whole board gets filled up without an SOS
appearing consecutively anywhere, the game is a draw.
Wythoff’s Game.
The positions of the Wythoff’s game are given by a queen on a
chessboard. Players, sitting on the same side of the board, take turns
moving the queen. But the queen may only be moved vertically down, or
horizontally to the left or diagonally down to the left. When the queen
reaches the lower left corner, the game is over and the player to move
last wins.
Wythoff’s Game.
The positions of the Wythoff’s game are given by a queen on a
chessboard. Players, sitting on the same side of the board, take turns
moving the queen. But the queen may only be moved vertically down, or
horizontally to the left or diagonally down to the left. When the queen
reaches the lower left corner, the game is over and the player to move
last wins.
Turning Turtles
At each move a player chooses an "O" and turns it into an "X". At the
same time this player may, if he so wishes, change a letter in any other
square to the left from the first one. In the left square, the player is
allowed to turn "O" into "X" and also "X" into "O". To perform a move,
the player should first click under the square he plans to change. You
can't undo your moves. The player to make the last move wins.
Turning Turtles
At each move a player chooses an "O" and turns it into an "X". At the
same time this player may, if he so wishes, change a letter in any other
square to the left from the first one. In the left square, the player is
allowed to turn "O" into "X" and also "X" into "O". To perform a move,
the player should first click under the square he plans to change. You
can't undo your moves. The player to make the last move wins.
Northcott’s Game
In every row of a rectangular board, there are two checkers: one white
and one black. A move consists in sliding a single checker in its original
row without jumping over another checker. The player to make the last
move wins.
Northcott’s Game
In every row of a rectangular board, there are two checkers: one white
and one black. A move consists in sliding a single checker in its original
row without jumping over another checker. The player to make the last
move wins.
Nim
Two players take turns removing objects from distinct heaps. On each
turn, a player must remove at least one object, and may remove any
number of objects provided they all come from the same heap. The
person who makes the last move (i.e., who takes the last object) wins.
Nim
Two players take turns removing objects from distinct heaps. On each
turn, a player must remove at least one object, and may remove any
number of objects provided they all come from the same heap. The
person who makes the last move (i.e., who takes the last object) wins.
Misere Nim
Two players take turns removing objects from distinct heaps. On each
turn, a player must remove at least one object, and may remove any
number of objects provided they all come from the same heap. The
person who makes the last move (i.e., who takes the last object) loses.
Misere Nim
Two players take turns removing objects from distinct heaps. On each
turn, a player must remove at least one object, and may remove any
number of objects provided they all come from the same heap. The
person who makes the last move (i.e., who takes the last object) loses.
The Thirty-one Game
From a deck of cards, take the Ace, 2, 3, 4, 5, and 6 of each suit. These
24 cards are laid out face up on a table. The players alternate turning
over cards and the sum of the turned over cards is computed as play
progresses. Each Ace counts as one. The player who first makes the sum
go above 31 loses.
The Thirty-one Game
From a deck of cards, take the Ace, 2, 3, 4, 5, and 6 of each suit. These
24 cards are laid out face up on a table. The players alternate turning
over cards and the sum of the turned over cards is computed as play
progresses. Each Ace counts as one. The player who first makes the sum
go above 31 loses.
Hackenbush
Hackenbush is a two-player mathematical game that may be played on
any configuration of colored line segments connected to one another by
their endpoints and to a "ground" line. The game starts with the players
drawing a "ground" line (conventionally, but not necessarily, a
horizontal line at the bottom of the paper or other playing area) and
several line segments such that each line segment is connected to the
ground, either directly at an endpoint, or indirectly, via a chain of other
segments connected by endpoints. Any number of segments may meet at
a point and thus there may be multiple paths to ground.
On his turn, a player "cuts" (erases) any line segment of his choice.
Every line segment no longer connected to the ground by any path
"falls" (i.e., gets erased). According to the normal play convention of
combinatorial game theory, the first player who is unable to move loses.
Hackenbush
Hackenbush is a two-player mathematical game that may be played on
any configuration of colored line segments connected to one another by
their endpoints and to a "ground" line. The game starts with the players
drawing a "ground" line (conventionally, but not necessarily, a
horizontal line at the bottom of the paper or other playing area) and
several line segments such that each line segment is connected to the
ground, either directly at an endpoint, or indirectly, via a chain of other
segments connected by endpoints. Any number of segments may meet at
a point and thus there may be multiple paths to ground.
On his turn, a player "cuts" (erases) any line segment of his choice.
Every line segment no longer connected to the ground by any path
"falls" (i.e., gets erased). According to the normal play convention of
combinatorial game theory, the first player who is unable to move loses.