# Chess tournament

Question: Mr. and Mrs. Birla & Mr. and Mrs. Tata competed in a Chess tournament. Of the three games played:
1. In only the first game were the two players married to each other,

2. The men won two games and the women won one game.

3. The Birlas won more games than the Tatas.

4. Anyone who lost a game did not play a subsequent game. Who did not lose a game?

List out all the possibilities and remove the possibilities which contradict the given conditions.

There are only 3 possibilities:

1. Mr. Birla won one game, Mrs. Birla won one game and Mr. Tata won one game.

2. Mr. Birla one two games and Mrs. Birla won one game.

3. Mr. Birla won two games and Mrs. Tata won one game.

If (I) is correct, then Mr. Tata beats Mrs. Tata in the first game. Then Mr. Tata would have lost to either Mr. Birla or Mrs. Birla in the second game. And Mr. and Mrs. Birla would have played the third game which contradicts the statement (1). So (I) is not correct.

Similarly, (II) is not correct.

(III) is correct. Mr. and Mrs. Birla played the first game and Mr. Birla won the game. Mr. Birla won the second game against Mr. Tata and lost the third game against Mrs. Tata.

Thus, only Mrs. Tata did not lose a game.