Correct Answer: Eshan

Explanation: From the uniquely determined clockwise seating arrangement Bina → Eshan → Diya → Gaurav → Farhan → Chirag → Aarav, the child sitting immediately to the right of Bina is Eshan. This arrangement is fixed once the first three rounds are analysed using the left/right movement rules on a circle of seven, and no alternative seating satisfies all later rounds simultaneously.

Step wise Explanation

Step 1: Start with a blank 10-round table
Only given information at this point:
• Total rounds = 10
• Round 1 starts with Bina passing
• Round 10 ends with Chirag receiving

Step 2: Fill all information directly given in the question

From the table in the question, we fill pass types and receivers wherever explicitly mentioned. We also fill Bina as the passer in Round 1.

Here R2, R4, R6, and R8 are placeholders for unknown receivers.

Step 3: Use the rule “receiver of one round becomes passer of the next”

This rule applies to every round of the game. Filling passers using this continuity:

• Round 2 passer = Aarav
• Round 3 passer = R2
• Round 4 passer = Diya
• Round 5 passer = R4
• Round 6 passer = Aarav
• Round 7 passer = R6
• Round 8 passer = Gaurav
• Round 9 passer = R8
• Round 10 passer = Farhan

Step 4: Use Rounds 1–3 to assign relative positions and identify R2

Fix Bina at position 0.

Round 1: Bina → Aarav (immediately left = −1)So Aarav = 6.

Round 2: Aarav → R2 (second right = +2) So R2 = 1.

Round 3: R2 → Diya (immediately right = +1) So Diya = 2.

Among remaining children, only Eshan fits position 1 consistently with later constraints.
So R2 = Eshan.

Step 5: Use the Diya → Aarav loop (Rounds 4 and 5) to identify R4

Diya is at position 2 and Aarav is at position 6.
The Buck goes Diya → R4 → Aarav in two rounds.

Across Rounds 4 and 5, the Buck travels Diya → R4 → Aarav in exactly two moves.

This forces R4 to be Gaurav, but does not yet force the exact order of R1 vs R2 between R4 and R5 at this stage. Hence, we identify the receiver but keep the pass types open.

Step 6: Use Round 6 to identify R6

Round 6: Aarav → R6 is second to the left.
From Aarav (position 6), second to the left is position 4, which is Farhan.

So R6 = Farhan.

Step 7: Use Round 8 to identify R8

Round 8: Gaurav → R8 is immediately to the left.
From Gaurav (position 3), immediately left is Diya (position 2). So R8 = Diya.

Step 8: Fix remaining pass types

From Diya (2) to Farhan (4) in Round 9, both R2 and R1 are structurally possible without enforcing deeper constraints.

From Farhan (4) to Chirag (5) in Round 10, both immediate left/right conventions can exist depending on chosen orientation.

Final working table:

Correct Answer: Chirag

Explanation: In the final clockwise order, Eshan occupies position 1. Moving third to the left corresponds to a shift of −3 on the circle, i.e. from position 1 to position 5. The child at position 5 is Chirag. This answer relies on the uniquely oriented seating that fits all rounds, not merely on local adjacency assumptions.

Step wise Explanation

Step 1: Start with a blank 10-round table
Only given information at this point:
• Total rounds = 10
• Round 1 starts with Bina passing
• Round 10 ends with Chirag receiving

Step 2: Fill all information directly given in the question

From the table in the question, we fill pass types and receivers wherever explicitly mentioned. We also fill Bina as the passer in Round 1.

Here R2, R4, R6, and R8 are placeholders for unknown receivers.

Step 3: Use the rule “receiver of one round becomes passer of the next”

This rule applies to every round of the game. Filling passers using this continuity:

• Round 2 passer = Aarav
• Round 3 passer = R2
• Round 4 passer = Diya
• Round 5 passer = R4
• Round 6 passer = Aarav
• Round 7 passer = R6
• Round 8 passer = Gaurav
• Round 9 passer = R8
• Round 10 passer = Farhan

Step 4: Use Rounds 1–3 to assign relative positions and identify R2

Fix Bina at position 0.

Round 1: Bina → Aarav (immediately left = −1)So Aarav = 6.

Round 2: Aarav → R2 (second right = +2) So R2 = 1.

Round 3: R2 → Diya (immediately right = +1) So Diya = 2.

Among remaining children, only Eshan fits position 1 consistently with later constraints.
So R2 = Eshan.

Step 5: Use the Diya → Aarav loop (Rounds 4 and 5) to identify R4

Diya is at position 2 and Aarav is at position 6.
The Buck goes Diya → R4 → Aarav in two rounds.

Across Rounds 4 and 5, the Buck travels Diya → R4 → Aarav in exactly two moves.

This forces R4 to be Gaurav, but does not yet force the exact order of R1 vs R2 between R4 and R5 at this stage. Hence, we identify the receiver but keep the pass types open.

Step 6: Use Round 6 to identify R6

Round 6: Aarav → R6 is second to the left.
From Aarav (position 6), second to the left is position 4, which is Farhan.

So R6 = Farhan.

Step 7: Use Round 8 to identify R8

Round 8: Gaurav → R8 is immediately to the left.
From Gaurav (position 3), immediately left is Diya (position 2). So R8 = Diya.

Step 8: Fix remaining pass types

From Diya (2) to Farhan (4) in Round 9, both R2 and R1 are structurally possible without enforcing deeper constraints.

From Farhan (4) to Chirag (5) in Round 10, both immediate left/right conventions can exist depending on chosen orientation.

Final working table:

Correct Answer: 2. Immediately to the right

Explanation: The question asks which pass type has a total number of occurrences that can be uniquely determined, meaning that its count remains invariant across all logically valid ways of completing the table. Even though some rounds allow ambiguity in pass type, enforcing the fixed seating arrangement and the continuity of the Buck forces the number of “immediately to the right” passes to be the same in every valid completion. Other pass types can vary depending on how the ambiguous rounds are resolved. Hence, only “immediately to the right” has a uniquely determined total count.

Step wise Explanation

Step 1: Start with a blank 10-round table
Only given information at this point:
• Total rounds = 10
• Round 1 starts with Bina passing
• Round 10 ends with Chirag receiving

Step 2: Fill all information directly given in the question

From the table in the question, we fill pass types and receivers wherever explicitly mentioned. We also fill Bina as the passer in Round 1.

Here R2, R4, R6, and R8 are placeholders for unknown receivers.

Step 3: Use the rule “receiver of one round becomes passer of the next”

This rule applies to every round of the game. Filling passers using this continuity:

• Round 2 passer = Aarav
• Round 3 passer = R2
• Round 4 passer = Diya
• Round 5 passer = R4
• Round 6 passer = Aarav
• Round 7 passer = R6
• Round 8 passer = Gaurav
• Round 9 passer = R8
• Round 10 passer = Farhan

Step 4: Use Rounds 1–3 to assign relative positions and identify R2

Fix Bina at position 0.

Round 1: Bina → Aarav (immediately left = −1)So Aarav = 6.

Round 2: Aarav → R2 (second right = +2) So R2 = 1.

Round 3: R2 → Diya (immediately right = +1) So Diya = 2.

Among remaining children, only Eshan fits position 1 consistently with later constraints.
So R2 = Eshan.

Step 5: Use the Diya → Aarav loop (Rounds 4 and 5) to identify R4

Diya is at position 2 and Aarav is at position 6.
The Buck goes Diya → R4 → Aarav in two rounds.

Across Rounds 4 and 5, the Buck travels Diya → R4 → Aarav in exactly two moves.

This forces R4 to be Gaurav, but does not yet force the exact order of R1 vs R2 between R4 and R5 at this stage. Hence, we identify the receiver but keep the pass types open.

Step 6: Use Round 6 to identify R6

Round 6: Aarav → R6 is second to the left.
From Aarav (position 6), second to the left is position 4, which is Farhan.

So R6 = Farhan.

Step 7: Use Round 8 to identify R8

Round 8: Gaurav → R8 is immediately to the left.
From Gaurav (position 3), immediately left is Diya (position 2). So R8 = Diya.

Step 8: Fix remaining pass types

From Diya (2) to Farhan (4) in Round 9, both R2 and R1 are structurally possible without enforcing deeper constraints.

From Farhan (4) to Chirag (5) in Round 10, both immediate left/right conventions can exist depending on chosen orientation.

Final working table:

Correct Answer: Gaurav

Explanation: In the fully reconstructed path, Gaurav receives the Buck in exactly two rounds (Rounds 4 and 7). Importantly, even while some receiver counts remain ambiguous during partial solving, Gaurav’s count becomes fixed due to the structure of the passes around him and the forced left passes involving his position. Thus, among the listed options, only Gaurav’s number of receptions can be uniquely determined.

Step wise Explanation

Step 1: Start with a blank 10-round table
Only given information at this point:
• Total rounds = 10
• Round 1 starts with Bina passing
• Round 10 ends with Chirag receiving

Step 2: Fill all information directly given in the question

From the table in the question, we fill pass types and receivers wherever explicitly mentioned. We also fill Bina as the passer in Round 1.

Here R2, R4, R6, and R8 are placeholders for unknown receivers.

Step 3: Use the rule “receiver of one round becomes passer of the next”

This rule applies to every round of the game. Filling passers using this continuity:

• Round 2 passer = Aarav
• Round 3 passer = R2
• Round 4 passer = Diya
• Round 5 passer = R4
• Round 6 passer = Aarav
• Round 7 passer = R6
• Round 8 passer = Gaurav
• Round 9 passer = R8
• Round 10 passer = Farhan

Step 4: Use Rounds 1–3 to assign relative positions and identify R2

Fix Bina at position 0.

Round 1: Bina → Aarav (immediately left = −1)So Aarav = 6.

Round 2: Aarav → R2 (second right = +2) So R2 = 1.

Round 3: R2 → Diya (immediately right = +1) So Diya = 2.

Among remaining children, only Eshan fits position 1 consistently with later constraints.
So R2 = Eshan.

Step 5: Use the Diya → Aarav loop (Rounds 4 and 5) to identify R4

Diya is at position 2 and Aarav is at position 6.
The Buck goes Diya → R4 → Aarav in two rounds.

Across Rounds 4 and 5, the Buck travels Diya → R4 → Aarav in exactly two moves.

This forces R4 to be Gaurav, but does not yet force the exact order of R1 vs R2 between R4 and R5 at this stage. Hence, we identify the receiver but keep the pass types open.

Step 6: Use Round 6 to identify R6

Round 6: Aarav → R6 is second to the left.
From Aarav (position 6), second to the left is position 4, which is Farhan.

So R6 = Farhan.

Step 7: Use Round 8 to identify R8

Round 8: Gaurav → R8 is immediately to the left.
From Gaurav (position 3), immediately left is Diya (position 2). So R8 = Diya.

Step 8: Fix remaining pass types

From Diya (2) to Farhan (4) in Round 9, both R2 and R1 are structurally possible without enforcing deeper constraints.

From Farhan (4) to Chirag (5) in Round 10, both immediate left/right conventions can exist depending on chosen orientation.

Final working table: