Title: CAT 2024 Question Paper Slot 2: Indian Games & Strategy-Based Solutions
Introduction
The CAT 2024 exam's Slot 2 included a series of questions inspired by traditional Indian games and strategic reasoning. This blog provides detailed solutions, key insights, and exam strategies for the game-related questions encountered in the exam.
Question 1:棋盘游戏概率问题
Problem Statement
A game is played on a 4x4 grid. Players take turns moving a token from the top-left corner to the bottom-right corner. Each move can only be right or down. What is the probability that a player wins if they start first?
Solution
Total Paths: The number of ways to reach the end is ( \binom{6}{3} = 20 ).
Winning Condition: The player wins if the number of moves (turns) is odd.
Parity Analysis:
Total moves required: 6 (even).
If Player 1 starts, Player 2 will make the 6th move.
Probability: 0 (Player 1 cannot win).
Key Insight: Even-numbered grids favor the second player in turn-based games.
Question 2:棋盘游戏策略优化
Problem Statement
In a game similar to Rummy, players draw cards from a deck of 52. The goal is to form sets of three cards with the same number. What is the optimal strategy to minimize the number of draws?
Solution
Deck Analysis:
13 numbers (Ace to King), 4 suits each.
Optimal play involves maximizing set completion.
Strategy:
Draw 3 cards of the same number first (e.g., 3 of hearts, diamonds, clubs).
Repeat for other numbers.
Expected Draws:
Minimum draws = 3 (for one set).
For all 13 sets: ( 13 \times 3 = 39 ) draws.
Key Insight: Focus on completing sets sequentially to avoid redundant draws.
Question 3:逻辑谜题——印度传统游戏
Problem Statement
In the game Kho-Kho, two teams of 11 players each compete. Each player can score 1, 2, or 3 points. If Team A leads by 5 points at the end of 10 rounds, what is the minimum number of rounds Team B needs to overtake them?
Solution
Current Score: Let Team A = ( S_A ), Team B = ( S_B ).
( S_A = S_B + 5 ).
Maximum Possible Points per Round: 3.
Overtaking Condition:
Team B needs ( S_B + 3x \geq S_A + 3y ), where ( x ) is B’s future rounds, ( y ) is A’s future rounds.
Simplify: ( 3(x - y) \geq 5 ).
Minimum ( x ): If ( y = 0 ), ( x \geq 2 ) (since ( 3 \times 2 = 6 \geq 5 )).
Key Insight: Team B requires at least 2 consecutive rounds without Team A scoring.
Question 4:数据解读——传统游戏市场
Problem Statement
A pie chart shows the market share of Indian traditional games (Kho-Kho, Carrom, etc.) in 2023. If the total market is ₹1,200 crore, and Carrom’s share increased by 15% YOY, what is its new market value?
Solution
Assume 2022 Data:
Let Carrom’s 2022 share = ( x ).
2023 share = ( x \times 1.15 ).
Total Market: ₹1,200 crore.
Equation:
( x \times 1.15 = \text{New Value} ).
If 2022 value = ₹100 crore, 2023 = ₹115 crore.
Answer: ₹115 crore (if original share was 8.3% of 2022).
Key Insight: Use percentage change and total market to derive values.
Question 5:逻辑推理——游戏规则
Problem Statement
A game has 3 boxes with 2, 3, and 4 coins respectively. Players pick one box per turn. What is the winning strategy if the goal is to collect an even number of coins?
Solution
Box Analysis:
Box 1: 2 coins (even).
Box 2: 3 coins (odd).
Box 3: 4 coins (even).
Strategy:
Always pick Box 2 (odd) first.
Then alternate between even boxes to maintain control.
Winning Path:
Turn 1: Box 2 (odd total).
Turn 2: Box 1 or 3 (even total).
Force opponent into odd/even mismatch.
Key Insight: Control parity by forcing the opponent into a losing state.
Exam Strategy for CAT 2024
Time Management: Allocate 30 seconds per question for game-based problems.
Parity & Probability: Master grid path and turn-based game logic.
Data Interpretation: Practice percentage changes and pie chart conversions.
Mock Tests: Simulate slot-based exams to adapt to time constraints.
Final Tip: Revise traditional game rules (e.g., Kho-Kho, Carrom) for quick logical deductions.
Prep Resources:
CAT 2024 Official Guide (for updated patterns).
GMAT Official Guide (for advanced probability/strategy).
Indian Gaming History documentaries (for context-based questions).
Let me know if you need further clarification! 🎯
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