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# Join Five

Join Five is a paper and pencil game for one or two players, played on a plus-shaped grid of dots (Figure 1). The origin of the game is unknown, as are other potential names for it.

## How to play

Draw the initial grid as shown in Figure 1.

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

1. No part of the new line can retrace any portion of a previously drawn line.
2. Exactly one of the five dots covered by the new line is missing from the grid before the line is drawn. This missing dot (which can be at either end of the new line, or somewhere in the middle) is also drawn during the turn.

In other words, make a five-segment line from four dots, and draw in the fifth.

Figure 2 shows the grid after one turn. Figure 3 shows the same grid after three additional turns. The game ends when no more segments can be drawn on the grid (Figure 4).

## Scoring

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.

## Strategy/Analysis

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.

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