VARC 2022 Slot 3: Indian Game Logic Puzzle Solution
Problem Statement (Hypothetical reconstruction based on common VARC patterns):
In a traditional Indian game called "Kho-Kho," two teams of 11 players each compete. Each team has a captain and a vice-captain. During a match, a player can be in one of three states: Active (A), Substituted (S), or Injured (I). The game rules state:
A team must have at least 7 Active players to start a quarter.
If a player is Injured (I), they cannot be promoted back to Active (A) in the same quarter.
Substituted (S) players can be recalled to Active (A) if they meet specific conditions.
Given the following scenario for Team X before the second quarter:
6 Active (A), 3 Substituted (S), 2 Injured (I).
Captain and Vice-Captain are both Active.
How many minimum players need to be recalled from Substituted (S) to Active (A) to meet the 7 Active requirement? Justify your answer.
Solution:
Initial State Analysis:
Total players: 11
Active (A): 6 (including Captain and Vice-Captain)
Substituted (S): 3
Injured (I): 2
Key Constraints:
Requirement: ≥7 Active players for the quarter.
Injured players (I) cannot be promoted.
Substituted (S) players can be recalled to Active (A) under rules not explicitly defined here, but assume:
A recalled Substituted player (S→A) must not have been previously injured.
Captain and Vice-Captain remain Active unless injured.
Gap Calculation:
Current Active: 6
Required Active: 7
Minimum recalls needed: (7 - 6 = 1)
Validation:
Recall 1 Substituted (S) player → New Active count = 7.
Captain and Vice-Captain remain Active (no injury).
Injured players (I) remain unaffected.
Answer:
(\boxed{1})
Alternative Scenarios (if constraints differ):
If recalled Substituted players require a "rest period," additional calculations may apply.
If Captain/Vice-Captain could be demoted, but rules specify they must stay Active.
Note: This solution assumes hypothetical rules for clarity. Actual VARC questions may include nuanced conditions (e.g., substitution limits per quarter). For precise answers, refer to the original exam paper.
Let me know if you need further refinements!
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