In a game of chess, the moves of white and black pieces

airan · Last edited by airan on Thu Jul 24, 2008 8:20 am; edited 1 time in total

In a game of chess, the moves of white and black pieces alternate, with white pieces having the first move. During a certain chess tournament, the white pieces have made 2319 moves altogether, while the black pieces have made a total of 2315 moves. In every game, either the white side wins,black side wins or there is a draw. If it is impossible for the losing side to make the last move in a game, which of the following could be true about the tournament ?

I The black side lost 5 games
II The black side won more games than the white side
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

OA is D

sudhir3127 · Posted: Tue Jul 22, 2008 7:41 am Post subject:

IMO A.. whats the OA?

egybs

Unless I'm missing something, the answer is D:

When white wins: white gets 1 more move than black
when black wins: both have the same number of moves
If there's a draw: either white gets one more move, or they have an even number of moves.

I) Impossible since black losing 5 games, means white wins 5 games leading to white having 5 more moves. Since we're looking for a delta of 4 (2319-2315=4), and since there's no way for black to get extra moves, no matter what happens in the other games, black can't have less than a delta of 5.

II) This is very possible. Black winning games is meaningless for the delta... As long as white wins or draws (where it moves last) exactly 4 games.

III) Also possible. Recall that a draw can result in either the same number of moves each (if black moves last), or +1 move for white (if white moves last)... so as long as white has 4 draws where it moves last, every game can be dawn.

So II and III only... D

egybs · Posted: Tue Jul 22, 2008 8:44 am Post subject:

I should also mention... you can just rephrase the question based on the stem and just see how the answers match up... this would save you from having to think up situations...

We know that the delta is 4 (2319-2315=4)... which means that white must have ended the game 4 more times than black.

Because of these rules:

pepeprepa · Posted: Tue Jul 22, 2008 8:52 am Post subject:

I don't catch the thing about the draw.
When there is a draw they both have the same number of moves or it stops at any moment, it can be +1 for white or +1 for black?
In the case of the second one hypothesis, I II and III are possible.

pepeprepa · Posted: Tue Jul 22, 2008 8:54 am Post subject:

Ok thank you egybs
So it is II and III

egybs · Posted: Tue Jul 22, 2008 8:59 am Post subject:

Think about it, how can black have an extra move?

Either the game ends on a white move or ends on a black move. If it ends on a white move, then white has moved an extra time. If it ends on a black move then they have both had an even number of moves...

For black to have a +1, it would need to move twice in a row, which it can't.

If it's still not clear consider each pair of moves to be a round. In every normal round there will be one white move and one black move. In the special case of a winning or drawing round one of the following will happen. Remember that before each round starts, both sides have played the same number of moves.

-White wins: In this case black will not get to play that round... so + 1 for white.
-Black wins: In this case, white has already played that round, so it's a +0 for both.
-Draws: There are two kinds of draws... one where white moves last... in which case, black doesn't get to play in that round, so +1 for white... and one where black moves last... where white has already moved in the round, so there's a +0 for both.

Does this help?

This is a cool question... where did it come from?

parallel_chase

egybs

Overly simplistic... You're confusing what happens in DS with these kinds of questions... In DS, the two pieces of info are consistent...

In this case, they are merely offering three different situations and asking which are possible given the stem... there's no need for them to all jive.

egybs

Also, reread the question... They aren't saying MUST BE TRUE... They're saying COULD BE TRUE.

Regardless, even in DS.. I wouldn't try to find this kind of shortcut.. it'll get you into trouble. Just answer the question instead...

parallel_chase · Posted: Tue Jul 22, 2008 1:13 pm Post subject:

You are absolutely right. I did about 3 such questions from OG.
I dont how I made such a blunder, maybe because its 3 am in the morning.

Thanks for this. Really appreciate it.

egybs · Posted: Tue Jul 22, 2008 1:52 pm Post subject:

not a problem!