Tuesday, December 23, 2008

Uncooked Spaghetti And Square Meatballs

(This game sounds familiar. Is it original?)

This is a game for 2 players.

Start with a carefully drawn n-by-n grid.

The players take turns completely filling in a total of n squares of the grid. (So, the first player to move fills in ceiling(n/2) squares, and the second player to move fills in floor(n/2) squares.)

After the squares are filled in, then the second player who filled in the squares is the first player to move in the next phase of the game.

The players take turns. On each turn a player draws a straight line from any empty vertex on the edge of the grid (where a grid-line meets the grid's perimeter) to any other empty vertex on any other edge of the grid.
By "empty" vertex, I mean a vertex that has not yet had a line drawn to it or from it in this phase of the game.

No line may pass through any filled-in square. But a line may touch a filled-in square (along an edge or touching at a corner).

(Also, lines may be vertical or horizontal. For this reason, I suggest that the grid be lightly drawn.)

Every time a line passes through a previously drawn line (previously drawn by either player in the second phase of the game) then the player's OPPONENT gets a point for each line crossed by the player's line.

Players move until there are no more possible lines that can be drawn under the rules.
(If a player claims that he/she cannot move any more, then the player's opponent may challenge this assertion and find, if possible, a path the player's line can indeed follow.)

Highest score wins.

Leroy Quet

PS: See the post (to my blog "Amorphous Trapezoid") about games-related poetry at:

Palindromic Card Game

This is a card game for 2 players. (Although this game doesn't technically require cards, using them makes the game easier to play.)

Start with 2n cards, n red and n black cards. (You can play with a standard deck {no jokers}, letting n be 26, and all spades and clubs are black, all hearts and diamonds are red. All that matters in this game is the colors of the cards' suits.)

Deal n cards to each of the players.

Players arrange their n cards in any order in a row, face up.
(One row of cards per player.)

After the cards are arranged, each player then tries to find as many distinct palindromes (symmetric patterns of of redness and blackness) within their opponent's row of cards, where each palindrome starts and ends with a red card. By DISTINCT palindrome I mean that each particular arrangement of reds and blacks counts only once. (Also, different distinct palindromes may share some of the same cards. And a palindrome may consist of exactly one red card.)

For example, if we have an n of 12 and we have the following row:


Then the palindrome (R B B R) would be counted once, even though it occurs twice in the row.
(The palindrome (BBRBB) would not count at all because it starts and ends with black cards.)

A player gets this many points:

(number of red cards in the player's row) - (number of DISTINCT palindromes found by the player's opponent in the player's row).

(This score will always be 0 or higher.)

Highest score wins.

Leroy Quet

PS: See the post (to my blog "Amorphous Trapezoid") about games-related poetry at:

Friday, December 12, 2008

"Maze" Of Polygonal Sections, Game

This game has elements in common with an earlier game of mine, Slice And Fill.

This game will work with any number of players.

Start with an n-by-n grid lightly and carefully drawn on paper.

Darken in the 4 grid-lines that form the square boundary of the grid. (All of the vertexes along the grid's edge are thereafter each considered to be drawn-to by a line-segment.)

Players take turns drawing straight line-segments, one segment per move, each segment drawn from any vertex of the grid that has a line segment passing through it or terminating at it, to any vertex that touches no line-segments, such that the line segments don't cross any others or coincide with any others.
(Any number of segments may be drawn FROM any single vertex. Line-segments may be diagonal and of any slope. Each line-segment may pass through any number of vertices. But, I repeat, line segments must each be drawn from a vertex of the grid to another vertex of the grid, not from an intersection of a line-segment and a grid-line if that intersection is not a vertex of the grid.)
The first line-segment (after the perimeter of the grid is filled in) is drawn from a vertex along the edge of the grid, of course.

When all vertexes of the grid are touching line-segments, we have a maze (without an entrance or exit), and then the next phase of the game begins.

One player starts the second phase by filling in any "section" of the subdivided grid. A section is defined by* the lines of the grid and/or by straight line-segments drawn by players (a section may be a square, or it may be a polygon which is a subset of a square).
*[By "where the section is defined by...", I mean "where the section is BORDERED by" the lines of the grid and/or by straight line-segments drawn by players. There are no internal line-segments within any given "section".]

Then the players take turns filling in, if possible, any UNFILLED section that is immediately adjacent to the previously filled in section (filled in by another player) and that is not separated from the previously filled in section by a line-segment drawn in the earlier phase of the game. (So, consecutively filled sections must not only be adjacent, but must be in the same "corridor" of the maze.)
If a section can be filled in under the rules, then a section must be filled in.

If, however, a section cannot be filled in by a player (either because it is surrounded by already filled in sections, or it is at one of the maze's dead-ends), then the previous player to move gets a point. The player who cannot fill in a section under the rules above then fills in any unfilled section (so as to start a new string of filled in sections).

The game continues until all sections are filled in.

The player with the greatest number of points wins.

Leroy Quet

Tuesday, December 2, 2008

Co-Compositeness (a game)

This is a game for any number of players. Start with an n-by-n grid, where n is larger if there are more players. (I suggest an n of at least 16 if there are 2 players.)

The first player to move places a 1 in any of the grid's squares.

Players take turns placing numbers in the grid's squares as follows:

*Each player places in a grid-square the next higher odd integer than the (odd) integer previously put in a square by the previous player to move. (So, let m be the number of total moves made by all the players so far; then the next player to move places a {2m+1} in the next square.)

*Players place the (odd) integer in a square that is immediately adjacent (in any of the 8 directions of: above, below, left of, right of, or diagonally) to the square the previous (odd) number was last put inside.

*Each integer is either placed in an empty square or in a square that already contains just one number that is NOT coprime to the integer the player is now placing in the square. There may be no more than 2 integers in any one square.

Every time a player places an integer in a square with an integer already in it, then that player gets a point. (Any pair of integers in the same square must be "co-composite", ie non-coprime.)

Players continue filling in the squares until a player cannot move anywhere. (If a player can move, then the player must move.) Then the game is over.

Highest score wins.

(Note: Part of the strategy of this game might be for a player to try to force an early ending to the game if that player has the highest score so far.)

Leroy Quet