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Net Coverage (Posted on 2012-02-02) Difficulty: 3 of 5
Net Coverage is a game played on a 13x19 grid. On each turn, a player places a cube net on the board.

How to Play:

1) The "starting points" (labeled 'S') are the center edges of the 13-unit sides of the board. Each player's first net must be adjacent to his respective starting point.

2) Each subsequent net placed must be adjacent to at least one other net the player has played.

3) Play alternates between the two players until one player cannot make another play. The other player continues to play until she, too, can no longer play. Then the game is over. In the example below, turns 1 through 13 happen first, then player two plays O, player one plays A, two plays P, one plays B, two plays Q, one plays C, and since player two has no more moves, player one continues by playing D through N.

4) The player who goes first is trying to create a board where at least 70% (or at least 173) of the squares are occupied by either player's nets. The player who goes second is trying to create a board where at least 30% (or at least 74) of the squares are NOT occupied be either player's nets.








S













13



Q

12





2






11






A


O P 6




4





5 7 B













10
I
L C



8 3






K





J
D



H H

9





1 G E

N
M F















s






In the above example, after 13 moves (1 through 13), the two players have "claimed" their areas of the board. Then, the first player tried to place as many nets as possible on her side, and the second player tried to place as few nets as possible on his side. Once the second player plays O, P, and Q, he has no more moves, so the first player continues playing until she has no more moves. Since the game board above has 180/247 or 72.9% filled, which is greater than 70%, Player 1 wins.

What is the optimal strategy for this game? Would you rather be player 1 or player 2?

No Solution Yet Submitted by Dustin    
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Comments: ( Back to comment list | You must be logged in to post comments.)
Secondary consideration Comment 2 of 2 |
I fear that I misunderstood the thrust of Para 4.
Player 1 is trying force for as much board coverage as possible whereas Player 2 is trying to force as much void as possible.

Notwithstanding that, Player 2 needs to attempt some control over the centre of the board whilst placing nets with as much free space between them.  Player 1 however needs to try to take control of the centre of the board but with nets placed as compactly as possible.

Optimum strategy?  Player preference?


Aside:  Ooops!  There is a double "H", can't fix it personally but it offers nothing other than decreasing real estate :-(

Edited on February 3, 2012, 7:52 am
  Posted by brianjn on 2012-02-02 20:42:23

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