Rules of the 6 games of the National Championship, 2004

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2. Amazonas

Author: Walter Zamkauskas

Material

• An 8×8 checkered board;
• 8 pieces (4 of each color);
• 56 marks of the same color.

Objective

Prevent the opponent from playing.

Rules

Each player has four Amazons initially arranged as follows:

On each turn, each player performs two actions:

1. moves an Amazon that moves in a straight line vertically, horizontally or diagonally as many squares as the player wishes, as long as there is no piece in its path (i.e., like the queen in chess);
2. then, place a mark on an empty square. However, this square must be within reach of the last Amazon moved (i.e., she could move to the square in a single move).

Since each move causes a square to disappear from the board, the game must end. The player who fails to complete his move loses.

An example of an opening turn: White moves the Amazon from f1 to c4 and places a marker on c7 (this is a valid move because the Amazon could move to c7). Then Black moves the Amazon from a6 to e6 and places a marker on e3.

In short, we could describe this turn as: 1. f1-c4(c7), a6-e6(e3).

References

• T. Tegos, The Game of Amazons, http://swiss2.whosting.ch/jenslieb/amazong/amazong.html

3. Dots and Squares

Material

• Sheet of paper with the dotted lines shown in the figure below;
• a pencil.

Objective

Get the most squares with your name.

Rules

Each player alternately joins two neighboring points with a horizontal or vertical segment. When one of them completes a square, he writes his initial inside the square and plays again. When a player has a move that completes a square, no is obliged to do so.

In the following example the first player managed to close a square (marking it, for example, with a THE). As he must play again, he has the possibility of closing three more.

References

• E. Berlekamp, J. Conway, R. Guy, Winning Ways, A.K. Peters
• E. Berlekamp, Dots-and-boxes: Sophisticated Child's Play, A.K. Peters, 2000

4. Hex

Authors: Piet Hein, John Nash

Material

• A board like the one in the figure below;
• 100 pieces (50 of each color).

Objective

Create a path that joins the two edges of your color.

Rules

The game starts on an empty board.

Each turn, each player places a piece of their color on an empty hexagon. The black player wins the game if he creates a path that connects the black edges (in the diagram, northwest and southeast). In turn, the white player wins the game if he creates a path that connects the white edges (in the diagram, northeast and southwest).

Color change: The second player, in his first move (if he sees an advantage in doing so) can take advantage of the move made by his opponent, forcing the change of colors.

In this example, Black wins the game (if it is his turn to move) by placing a piece on the g2 square:

References

• C. Browne, Hex Strategy: Making the Right Connections, A.K. Peters, 2000

5. Ouri

Material

• 48 seeds (or other small objects, such as hazelnuts or stones);
• board with 14 holes.

Objective

The objective of the game is to collect more seeds than your opponent. The player who collects 25 (or more) seeds wins.

Rules

On the board there are two rows, each with six circular holes, called squares, in which the seeds in play are located. Each end of the board is occupied by a larger hole, called a deposit, intended to store the seeds captured from the opponent during the game.

Two players take part in the game and they play alternately. Each player's deposit is the one on their right.

Movements

At the beginning of the game, 4 seeds are placed in each of the twelve squares.

The player who opens the game collects all the seeds from one of his holes and distributes them, one by one, in the following holes, in an anti-clockwise direction. This rule remains for all games.

When a house contains 12 or more seeds, the player makes a complete turn around the board, skipping the house where he started.

You cannot take seeds from houses that contain only one, while there are houses with two or more.

Captures

Players capture seeds in the following situations:

1. When, when placing the last seed in an opponent's house, the latter has two or three seeds left, the player removes them and places them in his own deposit.
2. If the house(s) before that also have two or three seeds, the player captures them and stores them in his/her deposit. The capture is stopped at the first house that does not have that number of seeds.

NOTE: If, when depositing the last seed in the opponent's house, there are four or more seeds left, the player cannot capture them. If the house is empty and there is one seed left after the move, there will also be no capture.

Supplementary rules

Supplementary rules apply when one of the players runs out of seeds:

• When a player makes a move and runs out of seeds, the opponent is forced to make a move in which he introduces one or more seeds on that player's side.
• If a player captures and leaves his opponent without seeds, he is forced to play again, in order to introduce one or more seeds into his opponent's spaces.

End of the match

When a player captures the most seeds — 25 or more — the game ends and that player wins.

When a player runs out of seeds and the opponent cannot play to introduce some seeds into that player's spaces, the game ends and the opponent collects the seeds that are in their spaces for their deposit. The player with the most seeds wins.

When there are few seeds on the board and a situation is created that repeats itself cyclically, without the players being able or wanting to avoid it, each player collects the seeds that are in their houses and places them in their respective deposits.

References

• http://ouri.ccems.pt

6. Pawns

Author: Bill Taylor

Material

• An 8×8 checkered board;
• 16 pieces (8 of each color).

Objective

Be the first to place one of your pawns on the last line or manage to stop your opponent from playing (either because you have no pawns or because you are trapped).

Rules

At the beginning of the game, the pawns are placed according to the following diagram:

White starts. Each player alternates moving a pawn. The pawns move like chess pawns, that is:

• They move to the square in front if it is empty (except on their first move, where they can move two squares).
• Capture an opponent's pawn if it is on one of the two diagonally facing squares (see figure: the pawn on e4 can capture f5 but cannot capture e5). Captures are not mandatory.
• Capture in passing (from French, en-passant): A pawn attacking a square crossed by an enemy pawn that has advanced two squares (i.e., has not yet moved) can capture this pawn as if it had moved only one square. This capture can only be made on the move following the advance (see the following figure: Black has moved the pawn from f7 to f5. If White wishes, he can capture this pawn in passage by moving from e5 to f6).

References

• http://www.di.fc.ul.pt/~jpn/gv/pawnographic.htm

I National Mathematical Games Championship (11/26/2004): list of first and second place winners in each of the twelve championships.

The Portuguese Mathematical Games Competition