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 beat player and the worst player are on the same side of the net.

Who is the best player?

The correct answer is Her brother.

Let us analyze the relationships and rules step-by-step to determine who the best player is.

Step 1: Identify the players and their sibling relationships
The four players are:
1. Lakshmi
2. Lakshmi's brother
3. Lakshmi's daughter
4. Lakshmi's son

Within this group, the sibling pairs are:
• Lakshmi and her brother
• Her daughter and her son

Step 2: Determine court positions from Clue (i)
Clue (i) states: "Lakshmi’s brother is directly across the net from her daughter."
Let us designate the two sides of the net as Side 1 and Side 2. If Lakshmi's brother is on Side 1, then her daughter must be on Side 2, positioned directly opposite him:
• Side 1: Lakshmi's brother
• Side 2: Her daughter (directly opposite the brother)

This leaves Lakshmi and her son to occupy the remaining two positions. This gives us two possible team configurations:
• Configuration 1: Side 1 has Lakshmi and her brother; Side 2 has the daughter and the son.
• Configuration 2: Side 1 has the son and the brother; Side 2 has the daughter and Lakshmi.

Step 3: Analyze Clue (ii) for both configurations
Clue (ii) states: "Her son is diagonally across the net from the worst player’s sibling."
Let us evaluate who is diagonally across from the son in each configuration:

• In Configuration 1:
Since the brother is directly across from the daughter, the player directly across from Lakshmi is the son. Therefore, the player diagonally across from the son is Lakshmi's brother. According to the clue, the brother must be the sibling of the worst player. Since Lakshmi is the brother's sibling, Lakshmi is the worst player.

• In Configuration 2:
Since the brother is directly across from the daughter, the player directly across from the son is Lakshmi. Therefore, the player diagonally across from the son is the daughter. According to the clue, the daughter must be the sibling of the worst player. Since the son is the daughter's sibling, the son is the worst player.

Step 4: Use Clue (iii) to find the best player
Clue (iii) states: "The best player and the worst player are on the same side of the net."

• Under Configuration 1:
The worst player is Lakshmi, who is on Side 1. Thus, the best player must also be on Side 1. The players on Side 1 are Lakshmi and her brother. Since Lakshmi is the worst player, her brother must be the best player.

• Under Configuration 2:
The worst player is the son, who is on Side 1. Thus, the best player must also be on Side 1. The players on Side 1 are the son and the brother. Since the son is the worst player, her brother must be the best player.

Regardless of which configuration is correct, the logical deduction consistently leads to the conclusion that Lakshmi's brother is the best player.