marcodonzelli wrote:
incognito1 wrote:
marcodonzelli wrote:
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 Incorrect. At the most, blacks lost 4 games.
II. Blacks won more games than whites Possible
III. All games ended in a draw Possible. That white made more moves doesn't indicate that those were necessarily wins (could be draws as well)
III only
I and II only
I and III only
II and III only
I, II, and III
(D)
OA is D. can you explain in detail?
It's all about counting the number of games that end on either side. 4 games end with white being the last player, and 2315 end with black being the last player.
Let [NW] = number of whites moves, [NB] = number of blacks moves
Consider a single game of chess; since whites start, blacks can either win or draw on their turn. In that case:
[NB] = [NW]
Similarly, whites can win or draw on their turn. In that case:
[NW] = [NB] + 1
We're given the sum total of all white and black wins in a tournament. Clearly, whites have only won OR drawn 4 more games (2319 - 2315). Blacks, on the other hand have won OR drawn as many as 2315 games. Using this information, you can now solve the 3 choices.
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