Subdivide And Acquire Game

Here is a game for any plural number of players. Start with an n-by-n grid drawn on paper, where n is larger if there are more players.
Each player has a colored pencil of unique color.

In the first part of the game, players take turns drawing straight line-segments -- one line-segment each turn. A player can draw a line-segment from either the edge of the grid at a vertex, or from the end of another line-segment. (Multiple line-segments can join at one point.) The line-segments are drawn to any vertex of the grid (either empty or already occupied by a line segment), such that no line-segment is drawn through another segment or along another segment or through a vertex occupied by line-segments. (Although, as I said, a line-segment may end at a vertex already occupied by another segment.)

After the grid is subdivided into n*(number of players) sections, the second part of the game begins.
Players take turns filling in sections of the grid with their colored pencils. After each player fills in n sections, the score is determined.

Players add up the total area of all the sections in each player's color, with the area of a grid-square being 1. (This may be tricky because some sections will most probably have non-integer areas.)

Let a player's total area be m; then the winner is the player where
number of divisors of floor(m) is the SMALLEST.


Thanks,
Leroy Quet