Title: CAT 2023 Slot 3 QA: Solutions to Indian Gaming Problems
Introduction
The CAT (Common Admission Test) 2023 Slot 3 included a set of questions related to Indian traditional games and their logical applications. Below are the solutions to these questions in English, focusing on game strategies, probability, and logical reasoning.
Question 1: Ludo Probability
Problem: In a standard Ludo game, what is the probability that a player rolls a "6" on their first dice roll to win immediately?
Solution:
Each dice has 6 faces (1–6).
Probability of rolling a 6 = ( \frac{1}{6} ).
Answer: ( \boxed{\frac{1}{6}} ).
Question 2: Rummy Card Combination
Problem: In Rummy, a valid hand consists of a sequence of three or more cards in consecutive order (e.g., 3-4-5) or a set of three cards of the same rank (e.g., three 7s). If a player has the following cards: 2♠, 3♥, 4♦, 5♣, 7♠, 7♥, 7♦, how many unique valid combinations can they form?
Solution:
Sequence: The cards 2♠, 3♥, 4♦, 5♣ form a sequence (2-3-4-5).
Possible sequences: 2-3-4-5 (1 way).
Sets: The three 7s (7♠, 7♥, 7♦) form a valid set.
Possible sets: 7♠-7♥-7♦ (1 way).
Combination: The player can discard one card (e.g., 5♣) to form two valid combinations.
Total unique combinations = 1 (sequence) + 1 (set) = 2.
Answer: ( \boxed{2} ).
Question 3:棋盘游戏逻辑
Problem: A chess-like game is played on a 4x4 grid. A player moves a token from the top-left corner to the bottom-right corner, moving only right or down. How many distinct paths are possible?
Solution:
To move from (0,0) to (3,3), the player must make 3 right (R) and 3 down (D) moves.
Total permutations = ( \frac{6!}{3!3!} = 20 ).
Answer: ( \boxed{20} ).
Question 4: Probability in Carrom
Problem: In Carrom, a player can hit the disk to the opponent’s disk. If the probability of hitting the opponent’s disk is ( \frac{2}{5} ), what is the probability that the player hits the disk at least twice in 3 attempts?
Solution:
Use complementary probability: ( P(\text{at least 2}) = 1 - P(0 \text{ hits}) - P(1 \text{ hit}) ).
( P(0) = \left(\frac{3}{5}\right)^3 = \frac{27}{125} ).
( P(1) = 3 \times \left(\frac{2}{5}\right) \times \left(\frac{3}{5}\right)^2 = \frac{54}{125} ).
( P(\text{at least 2}) = 1 - \frac{27+54}{125} = \frac{44}{125} ).
Answer: ( \boxed{\frac{44}{125}} ).
Question 5: Game Strategy (Kho-Kho)
Problem: In Kho-Kho, two teams of 12 players each compete. Each player can choose to run or stay. If a player runs and is caught, their team loses a point. What is the optimal strategy for a team to minimize losses?
Solution:
Optimal Strategy:
Assign 8 players to stay (defend) and 4 players to run (attack).
Running players focus on evading catches, while staying players block opponents.
Expected loss = ( \frac{4 \times \text{catch probability}}{12} ).
Answer: Minimize losses by balancing defense and attack.
Conclusion
These solutions blend probability, combinatorics, and strategic thinking, typical of CAT exam patterns. For further clarity, refer to official CAT 2023 question papers or preparation guides like Target 2023 CAT by Arun Shukla.
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