In a game of chess, the moves of whites and blacks alternate with whites having the first move. During a certain chess tournament whites have made 2319 moves altogether while blacks have made 2315 moves. If in any game the side that made the last move did not lose, which of the following can be true about the tournament?
I. Blacks lost 5 games
II. Blacks won more games than whites
III. All games ended in a draw	Choose the correct choice from the following options
A) III only
B) I and II only
C) I and III only
D) II and III only
E) I, II, and III
if white wins, white will always have more moves than black.   Win: White. Then, White &gt; Black.   If Black wins, the number of moves of both white and black will be the same.   Win: Black. Then, White (moves) = Black (moves).   Why? Because, white cannot have the last move and lose the game (from the question). And white always starts so it will be WB WB WB till blacks last move.   If it is a draw, either of these possibilities exists.   Win: Draw. White &gt; Black or Black = White.   Statement 1: Black lost 5 games. This is false because anyone who plays the last move cannot lose (from the question). IF black lost 5 games, white will have a clear lead of 5 moves. It is only 4 moves from the question.   Statement 2: This is possible. Imagine that they play about 150 games. 146 could be black wins (So black moves will be equal to white). then last 4 can be White wins (White moves &gt; Black moves).   Statement 3: All games are draws with white having the last move in only 4 of them . Possible   the answer is II and III only
<result>D</result>
In a game of chess, the moves of whites and blacks alternate with whites having the first move. During a certain chess tournament whites have made 2319 moves altogether while blacks have made 2315 moves. If in any game the side that made the last move did not lose, which of the following can be true about the tournament?
I. Blacks lost 5 games
II. Blacks won more games than whites
III. All games ended in a draw