Question 186
On a rectangular board $100 \times 300$ two people take turns coloring the uncolored cells. The first one paints yellow, the second one paints blue. The coloring is completed when every cell on the board is colored. A *sequence of* cells is a set of cells in which two consecutive cells share a common side (all cells in the sequence are different). Consider all possible sequences of yellow cells. The *result* of the first player is the number of cells in the sequence of yellow cells of maximum length. The first player's goal is to maximize the result, and the second player's goal is to make the first player's result as small as possible. Prove that if each player strives to achieve his goal, the first player's result will be no more than $200$.