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6 Strategy Game
Basic Concepts Variations of Nim
There are several interesting variations of the Nim game. The most popular
game is the Connect-the-Line-Segments. The style of the game is different
from Nim, but the strategy to win the game is the same: a player works
backwards to solve a problem.
The rules are shown below.
Rules Finish
Start
1. Two players take turns drawing a line segment connecting
one point to another.
2. The players must draw each line from the ending point of
the previous line drawn by the opponent.
3. A line segment can be drawn to the right or upwards and
can be of any length.
4. The player who connects the line to the finishing point first
wins.
Example Using the game board on the right, a two-player 9 4 1 Finish
game is played according to the following rules. Who 10 5 2 3
is more likely to win: the first or the second player? 11 6 7 8
12 13 14 15
Rules
1. Two players take turns moving a stone to the right or upwards.
2. The stone can be moved to as many spaces as a player wants. However,
the stone can only be moved in one direction.
3. The player who moves the stone to the finishing point first wins.
Class Notes
On a 2 2 game board, the (first player, second player) always wins. 1 Finish
On a 3 3 game board, if a player moves two spaces to the right and places 23
the stone on square 8, the next player can move spaces
upwards and win. If a player moves one space upwards and 4 1 Finish 4 1 Finish
places the stone on 5, the next player can move space(s) 5 23 5 23
to the (upwards, right) and place the stone on and win. 6 78 6 78
On this kind of game board, the (first player, second player) always wins. ,
Thinking backwards, the winning spaces on the original 4 4 game board are 2,
and . As the starting number is also winning space,
the (first player, second player) always wins.
50 NUMINO Challenge B1
Basic Concepts Variations of Nim
There are several interesting variations of the Nim game. The most popular
game is the Connect-the-Line-Segments. The style of the game is different
from Nim, but the strategy to win the game is the same: a player works
backwards to solve a problem.
The rules are shown below.
Rules Finish
Start
1. Two players take turns drawing a line segment connecting
one point to another.
2. The players must draw each line from the ending point of
the previous line drawn by the opponent.
3. A line segment can be drawn to the right or upwards and
can be of any length.
4. The player who connects the line to the finishing point first
wins.
Example Using the game board on the right, a two-player 9 4 1 Finish
game is played according to the following rules. Who 10 5 2 3
is more likely to win: the first or the second player? 11 6 7 8
12 13 14 15
Rules
1. Two players take turns moving a stone to the right or upwards.
2. The stone can be moved to as many spaces as a player wants. However,
the stone can only be moved in one direction.
3. The player who moves the stone to the finishing point first wins.
Class Notes
On a 2 2 game board, the (first player, second player) always wins. 1 Finish
On a 3 3 game board, if a player moves two spaces to the right and places 23
the stone on square 8, the next player can move spaces
upwards and win. If a player moves one space upwards and 4 1 Finish 4 1 Finish
places the stone on 5, the next player can move space(s) 5 23 5 23
to the (upwards, right) and place the stone on and win. 6 78 6 78
On this kind of game board, the (first player, second player) always wins. ,
Thinking backwards, the winning spaces on the original 4 4 game board are 2,
and . As the starting number is also winning space,
the (first player, second player) always wins.
50 NUMINO Challenge B1
