Title: 2017 Quant Slot 1: Analyzing Indian Math Game Strategies
Content (English):
In the 2017 Quant Slot 1 exam, participants faced a series of mathematical challenges inspired by traditional Indian games, requiring logical reasoning and numerical fluency. Below is a breakdown of key problems and solutions, focusing on strategies commonly used in Indian competitive exams.
Problem 1: Rummy Card Calculation
Task: Given a deck of 52 cards, calculate the probability of forming a valid Rummy sequence (three cards of consecutive values, e.g., 5-6-7) using exactly 5 cards from the hand.
Solution:
Total Combinations: ( C(52,5) = 2,598,960 ).
Valid Sequences:
Choose a starting value (Ace to 10): 10 options.
Select 3 consecutive values: ( \binom{4}{1} ) (suits) for each card.
Add a pair (remaining 2 cards): ( \binom{4}{2} ) for the pair value.
Total sequences: ( 10 \times 4^3 \times 6 \times 12 = 230,400 ).
Probability: ( \frac{230,400}{2,598,960} \approx 8.86% ).
Key Insight: Leverage combinatorial logic and account for overlapping suits/pairs.
Problem 2: Chaturanga Grid Optimization
Task: A 4x4 grid is divided into 16 cells. How many ways can a knight (moves L1-R2) place 8 knights such that none attack each other?
Solution:
Knight’s Move Constraints: Knights attack in 8 directions. On a 4x4 grid, maximum non-attacking knights = 8 (alternating cells).
Color Parity: Knights alternate between black/white cells. Total black cells = 8, white cells = 8.
Valid Placements: ( \binom{8}{8} \times \binom{8}{0} = 1 ) (fixed pattern).
Symmetry Adjustment: 2 patterns (mirror images).
Answer: 2 ways.
Key Insight: Use parity and constraints from game rules.
Problem 3: Monopoly Property Acquisition
Task: Calculate the expected number of turns to buy all 28 Monopoly properties with a starting budget of ₹100,000, given:
Each property costs ₹5,000–₹50,000 (avg ₹25,000).
10% chance to land on a property each turn.
Solution:
Total Cost: ( 28 \times 25,000 = ₹700,000 ).
Deficit: ( ₹700,000 - ₹100,000 = ₹600,000 ).
Expected Turns per ₹25,000: ( \frac{1}{0.1} = 10 ) turns.
Total Expected Turns: ( 600,000 / 25,000 \times 10 = 240 ).
Key Insight: Model probability as a linear approximation for large samples.
Common Pitfalls & Tips
Overcounting Combinations: Use multiplicative principles instead of additive.
Ignoring Game-Specific Rules: Always map problems to real-game mechanics (e.g., Rummy’s sequences).
Time Management: Prioritize questions with 2–3 step solutions first.
Final Score Target: 80% accuracy in slot 1 (quant-heavy) requires 15/20 correct answers.
Conclusion: Mastering Indian math games in exams demands blending traditional strategies (e.g., parity in Chaturanga) with modern combinatorics. Practice 20+ daily problems to automate calculations and improve speed.
Let me know if you need further clarification or additional problem sets!
|
