Lakshmi, her brother, her daughter and her son are badminton players. A game of doubles is about to begin: (i) Lakshmi's brother is directly across the net from her daughter. (ii) Her son is diagonally across the net from the worst player's sibling. (iii) The best player and the worst player are on the same side of the net. Who is the best player?

Here's a brief explanation: 1. **Understand the Setup:** There are four players: Lakshmi (L), her Brother (B), her Daughter (D), and her Son (S). A doubles game means two teams of two players each. Let's visualize the court: Player1 Net Player3 Player2 Net Player4 2. **Analyze Statement (i):** "Lakshmi's brother is directly across the net from her daughter." This means B and D are on opposite sides, in corresponding positions. For example: B Net D _ Net _ The remaining two players, L and S, will fill the other two spots. So, the teams are either {B, L} and {D, S} OR {B, S} and {D, L}. 3. **Test Option A: Her brother (B) is the best player.** * **From (iii):** "The best player and the worst player are on the same side of the net." If B is the best player, then the worst player (W) must be B's teammate. So, W is either L or S. * **Scenario 1: Assume L is the worst player.** Team 1: {B (Best), L (Worst)}. Team 2: {D, S}. Court setup (from i): B Net D L Net S * **Now check (ii):** "Her son is diagonally across the net from the worst player's sibling." Worst player = L (Lakshmi). L's sibling = B (her brother). So, (ii) means: Son (S) is diagonally across the net from Brother (B). In our setup, S is in the bottom-right position and B is in the top-left position. These are indeed diagonally across the net. This scenario is consistent. * (A second scenario where S is the worst player also works, but one consistent scenario is enough to confirm Option A.) 4. **Why other options are incorrect (briefly):** * If Daughter (D) is the best player, Son (S) would either be diagonally across from B or D. However, in all possible team combinations, S and B/D would end up on the same side of the net, contradicting "diagonally across". * If Son (S) is the best player, Son (S) would either be diagonally across from L (but they are directly across the net) or diagonally across from S himself (which is impossible). * If Lakshmi (L) is the best player, Son (S) would either be diagonally across from L (but they are directly across the net) or diagonally across from S himself (which is impossible). Since only "Her brother" (B) consistently satisfies all conditions, he is the best player. The final answer is A) Her brother.