Puzzle time - modified dots and boxes
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The game of Dots and Boxes begins with a rectangular grid of dots. Players alternate drawing edges that connect neighboring dots, vertically or horizontally. When a player completes a box, he or she labels it with his or her initial and moves again; when all the edges are drawn, the player with the most boxes wins.
Suppose we change the rules to allow a player who makes a box either to move again, or decline to do so. Show that the second player has a winning strategy if this game is played on a 4x6 grid (35 dots).
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