In a game of chess the moves of whites and blacks alternate

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.

Bunel,

I need your help in understanding the question.

whites: 2319 Moves
Black: 2315 Moves

what dos this means?

Is it talking about chess's black and white square boxes?

I can not be true as if 5 blacks lost then difference between two moves should be alteast 5 or more
II can be true
eg. 1 game won by Black move WB
all other games are tied...as WB or WB...W this can result in the move difference.
III can be true
all games are tied as WB or WB....W or WB....B this can also result in move difference
Answer is D

*Simple Words*
Total White Moves 2319
Total Black Moves 2314
As given white made the first move, if we take the difference of 2319-2314=4 means that upto 2314 moves black made the last move and since white has 04 more moves, we can safely assume that for 04 games white made the last move and won the game. So remaining games can be anything draw or black won.

Only II & III Possible is D

Official Solution:


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


A. III only
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III


Let's examine each option.

I. Blacks lost 5 games

Since the moves of whites and blacks alternate with whites having the first move, then the fact that the whites made 4 more moves than blacks, means that in only 4 games whites made the last move. Therefore, in all other games, blacks made the last move and since we know that the side that made the last move did not lose, then blacks could not have lost in any of the games but in these 4. So, the maximum number of games black could have lost is 3. Thus, I cannot be true.

II. Blacks won more games than whites

From above, we know that blacks had the last move in all but 4 games. Thus, blacks could not win in only those 4 games but they could have won in all other games. So, could have won more games than whites.

III. All games ended in a draw

The stem does not give any stipulation on draws, so any game, no matter whites had the last move or blacks could have ended in a draw. Hence, all games could have ended in a draw.


Answer: D

I. Black lost 5 games: It is important to note that the side that made the last move did not lose in any game. Since White made 4 more moves overall than Black, this means that in only 4 games White made the last move. In all other games Black made the last move. Therefore the maximum number of games Black could lose is 3. Thus, variant I cannot be true. In fact you can distracted by other games, I was reading reviews on highest payout online casinos and I liked it very much.
II. Black won more games than White did: Given that Black had the last move in all but 4 games, this means that Black could not win only those 4 games. However, they could have won all the other games. Consequently, it is possible that Black won more games than White did.
III. All games ended in a draw: The statement does not contain any restrictions on draws. Thus, in any game, regardless of whether White or Black had the last move, it could have ended in a draw. Hence, it is plausible that all games ended in a draw.