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Join Five


Join Five (also known as Morpion solitaire, Cross 'n' Lines or Line Game) is a paper and pencil game for one or two players, played on a plus-shaped grid of dots. The origins of the game are probably in northern Europe. References to the game first appeared in French publications in the 1970s. In addition to being played recreationally, the game has been the subject of theoretical studies and computer searches for solutions.

An initial grid of dots are drawn; a square of 4x4 dots, with a rectangle of 4x3 added to each side. The initial cross is outlined in some versions of the game.

During each turn, draw a straight line that is exactly five "dots" long, such that:

In other words, make a five-segment line from four dots, and draw in the fifth (unless it is saved to draw two dots in later turns).

The game ends when no more segments can be drawn on the grid.

In the two player version, the last player to draw a line segment is the winner. In the single player version, scoring is accomplished by counting the number of segments drawn, or by calculating the total area of the grid at the end of play.

In the outlined version, the number of accomplished turns is the score. This is usually kept in check by using tally marks. It is unknown if this can be continued indefinitely, but the game becomes progressively more difficult (up to a point?) once the initial grid has been used completely.

Strategy differs according to whether the game is played alone or against an opponent. In the first case, moves are optimized for the maximum number of possible turns; in the second case, the goal is to be "inefficient" with move selection to restrict the opponent's available moves.

The rules may be varied by requiring lines of 4 marked points in a row rather than 5, with a reduced starting configuration. Also, the "disjoint" variation of the game does not allow two parallel lines to share an endpoint, whereas the standard "touching" version does allow this.

For the "touching" version of the game with lines consisting of 5 marked points, the present record of 172 lines was established on 2010 August 16, using a Monte-Carlo search by algorithmist Christopher Rosin. This is six moves more than the previous 1976 record of 170 lines. The 1976 record was done by hand, and computer searches had not been able to approach this record despite substantial progress, until August 2010 when Christopher Rosin used a Monte-Carlo search to obtain a result of 172 moves, exceeding the 1976 record.


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