CAT 2023 Slot 1 Mock: Indian Game Problem-Solving Guide
Here’s a structured breakdown of how to approach game-based problems commonly found in CAT exams, with a focus on Indian-themed scenarios. This guide includes problem-solving strategies, common pitfalls, and sample solutions.
1. Understanding CAT Game Problems
CAT game problems often involve logical reasoning, permutations/combinations, and data interpretation. Indian-themed games might include:
Cultural festivals scheduling (e.g., Diwali, Holi)
Rural/urban resource allocation
Traditional games (e.g., Rummy, Ludo)
Historical/cultural puzzles
Key skills tested:
Logical flow construction
Prioritization and constraint management
Mathematical modeling
2. Step-by-Step Problem-Solving Framework
Step 1: Read the Question Carefully
Identify:
Players/agents (e.g., villagers, teams)
Rules (e.g., time windows, dependencies)
Constraints (e.g., "No two festivals can overlap")
Objective (e.g., "Maximize profit" or "Find the number of valid schedules")
Example:
"A village plans to host 4 festivals (Diwali, Holi, Id, Eid) over 30 days. Each festival lasts 3 days, and there must be at least 5 days between events. How many valid schedules are possible?"
Step 2: Model the Problem
Visual tools: Timeline charts, matrices, or tree diagrams.
Mathematical tools: Combinations, permutations, or equations.
Solution for the Example:
Adjust for gaps: With 4 festivals (each 3 days) and 5-day gaps:
Total days required = (4×3) + (3×5) = 12 + 15 = 27 days.
Remaining days = 30 - 27 = 3 days → Distribute these as "flexible gaps".
Calculate combinations:
Use stars and bars to distribute 3 flexible days among 5 gaps (before first festival, between festivals, after last festival).
Formula: ( \binom{3 + 5 - 1}{5 - 1} = \binom{7}{4} = 35 ).
Total schedules: 35 (ways to distribute gaps) × 4! (arrange festivals) = 35 × 24 = 840.
3. Common Indian Game Problems & Solutions
Problem 1: Traditional Game Strategy
"In a Rummy-like game, players draw 13 cards from a deck of 52 (divided into suits: Spades, Hearts, Clubs, Diamonds). A valid set is 3 cards of the same suit or 4 cards of the same number. What’s the minimum number of cards a player must discard to guarantee a valid set?"
Solution:
Pigeonhole Principle:
If a player draws 13 cards, the worst-case scenario:
3 suits × 4 numbers each = 12 cards (no duplicates).
13th card forces a duplicate → 1 card to discard.
Problem 2: Cultural Festival Allocation
"A city has 10 zones. Each zone must host exactly 2 festivals (Diwali or Holi). However, no two adjacent zones can host the same festival. How many ways can festivals be allocated?"
Solution:
Graph Coloring Analogy:
Zones = nodes; adjacency = edges.
First zone: 2 choices (Diwali/Holi).
Each subsequent zone: 1 choice (opposite of previous).
Total = ( 2 \times 1^{9} = 2 ).
Problem 3: Resource Distribution
"A farmer has 10 cows and 15 goats. He sells them in pairs (either 2 cows, 2 goats, or 1 cow + 1 goat). What’s the maximum number of pairs he can sell?"
Solution:
Optimization:
Sell as many 1C+1G pairs as possible: 10 cows limit to 10 pairs (uses 10 cows, 10 goats).
Remaining goats: 15 - 10 = 5 → 2 more pairs (2G + 1 leftover).
Total: 10 + 2 = 12 pairs.
4. Time Management Tips
15–20 seconds per simple game problem (e.g., Rummy).
1–2 minutes for complex scheduling/optimization problems.
Eliminate answer choices early using constraints.
5. Final Tips
Practice Indian-themed puzzles from past CAT papers (e.g., IIM Bangalore mock tests).
Use answer elimination for time-consuming problems.
Review combinatorics formulas (permutations, combinations, pigeonhole principle).
Let me know if you need further clarification or additional problem examples! 🧠📊
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