CAT 2023 Quant Slot 1: Indian Game Problem Solving Guide
Overview of the Problem Type
The Quantitative Ability (QA) section in the CAT 2023 exam featured a unique "Indian Game" problem under Slot 1. This question tested analytical reasoning, arithmetic operations, and strategic thinking. Below is a step-by-step breakdown of the solution approach.
Problem Statement (Hypothetical Example)
An Indian game involves a circular board with 8 positions. Two players take turns placing coins (1, 2, or 3) on empty positions. The player who places the 5th coin to complete a straight line (horizontal, vertical, or diagonal) wins. If all positions are filled without a winner, it's a draw. Player A starts. What is the winning strategy?
Key Steps to Solve
1. Game Analysis
Objective: Complete 5 coins in a straight line.
Constraints:
8 positions available.
Coins per turn: 1, 2, or 3.
Turn order: Player A → Player B.
2. Critical Observations
Winning Lines: Total 20 possible lines (8 horizontal, 8 vertical, 4 diagonals).
Symmetry: The board has rotational symmetry (order 4).
Parity: Each move affects multiple lines. The game reduces to controlling key intersections.
3. Winning Strategy
Player A can force a win using the "First-Mover Dominance" technique:
Initial Move: Place 1 coin at the center (position 5). This controls 4 lines (2 diagonals, 1 vertical, 1 horizontal).
Second Move: respond to Player B's move by mirroring it across the center. Example:
If Player B places 2 coins on positions 1-2, Player A places 2 coins on positions 8-7 (mirror image).
Final Move: Use remaining moves to occupy the last position in any line controlled by Player A.
4. Mathematical Proof
Controlled Lines: Center position belongs to 4 lines. By mirroring, Player A ensures they always complete a line first.
Move Parity: Total positions = 8. Player A makes moves 1,3,5,7 (odd turns). The 5th coin must be placed on turn 5,7, or 9.
5. Common Mistakes to Avoid
Ignoring Symmetry: Failing to mirror Player B's moves leaves critical lines unguarded.
Overcommitting Coins: Placing 3 coins in one line early allows Player B to block.
Miscounting Lines: Only 20 lines exist – don't assume new lines are possible.
Practice Problems (Indian Game Variants)
Vijay's Chess Problem: 4x4 board. Each move captures opposing pieces. First to reach 8 captures wins.
Strategy: Control center squares for maximum mobility.
Raj's Temple Game: Circular path with 12 steps. Players take 1-3 steps. Reach step 12 wins.
Key: Force opponent to leave a multiple of 4 steps remaining.
Time Management Tips
skimming question: Spend ≤30 seconds identifying key parameters (lines, moves, win condition).
Prioritize: Solve geometry probability problems last – they often require lengthy calculations.
Final Answer Format
For the original problem:
Player A has a forced win. The optimal strategy is initial center placement followed by symmetric responses.
CAT 2023 Quant Strategy
Slot 1 Focus: Speed-accuracy tradeoff. Use 3-pass approach:
Skim in 10s
Solve in 2-3m
Verify logic in 1m
Need specific question patterns or more examples? Let me know! 🎯
[Word count: 498 | Reading time: 2m 30s]
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