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by Bob Sidebotham

There's a little pencil and paper game, Tactics, played on a 4x4 grid.
The play starts with an empty grid. On each turn, a player can fill in
one to four adjacent squares, either horizontally or vertically. The
player who fills in the last square loses.

Here's a sample game to help clarify the above rules. The board
position at the end of each play is shown (best viewed in a
fixed-width font):

	First player   Second player
	
	  X X X X        X X X X       (Turn 1)
	  _ _ _ _        _ _ _ _
	  _ _ _ _        _ _ X _
	  _ _ _ _        _ _ X _
	
	  X X X X        X X X X       (Turn 2)
	  X X _ _        X X _ X
	  _ _ X _        _ _ X X
	  _ _ X _        _ _ X _
	
	  X X X X        X X X X       (Turn 3)
	  X X _ X        X X X X
	  _ _ X X        _ _ X X
	  _ _ X X        _ _ X X
	
	  X X X X        X X X X       (Turn 4)
	  X X X X        X X X X
	  X X X X        X X X X
	  _ _ X X        X _ X X
	
	  X X X X                      (Turn 5
	  X X X X                       Second
	  X X X X                       player
	  X X X X                       wins!)

Your task, should you choose to accept it, is to write a Ruby program
which, given only these rules, determines whether the first or second
player is bound to be the winner, assuming perfect play. It should do
this in a "reasonable" amount of time and memory--it should definitely
take under a minute on any processor less than 5 years old. Bonus
points if you can make the case that your program actually gets the
right answer for the right reason!