Скачать или смотреть Couple Handshakes: Combinatorics Interview Question in Python | QuantGuide IO

Solve the "Couple Handshakes" problem from QuantGuide IO with this step-by-step combinatorics tutorial! The problem: A room of four couples (8 people) greet each other by shaking hands, but each person does not shake hands with their partner. We’ll calculate the total number of handshakes, which turns out to be 24. We’ll break down the problem, use combinations to find the total handshakes, subtract the non-occurring handshakes, and verify with Python. Perfect for anyone prepping for a quant interview, math enthusiasts, or those learning combinatorics for interview questions!

🔍 *What You'll Learn:*
Understanding the Couple Handshakes problem setup
Using combinations to calculate total possible handshakes
Adjusting for the constraint (no handshakes between partners)
Computing the final result with Python

💻 *Solution Walkthrough:*
Total people: 8 (four couples).
Total possible handshakes if everyone shook hands with everyone else: \( C(8, 2) = \frac{8 \times 7}{2} = 28 \).
Non-occurring handshakes: Each person does not shake hands with their partner. There are 4 couples, so there are 4 pairs who don’t shake hands.
Total handshakes = Total possible handshakes - Non-occurring handshakes = \( 28 - 4 = 24 \).
Alternative approach: Each person shakes hands with 6 people (8 total - 1 partner - 1 self). Total handshakes = \( (8 \times 6) / 2 = 48 / 2 = 24 \) (divide by 2 since each handshake involves 2 people).
Final answer: 24 handshakes.

Python code to compute the handshakes
import math

total_possible_handshakes = math.comb(8, 2) # C(8, 2) = 28
non_occurring_handshakes = 4 # 4 couples, so 4 pairs don’t shake hands
total_handshakes = total_possible_handshakes - non_occurring_handshakes # 28 - 4 = 24
print(f"Total handshakes: {total_handshakes}")
Output: Total handshakes: 24

Alternative approach
people = 8
handshakes_per_person = 6 # Each person shakes hands with 8 - 1 (self) - 1 (partner) = 6 people
total_handshakes_alt = (people * handshakes_per_person) // 2 # (8 * 6) / 2 = 24
print(f"Alternative approach: {total_handshakes_alt}")
Output: Alternative approach: 24

🌟 *Why Solve Couple Handshakes?*
This problem is a classic combinatorics question, perfect for quant interview prep or math competitions! It teaches you how to handle constraints in handshake problems using combinations, a key skill for problem-solving in a quant interview setting. The total number of handshakes is 24, and we’ll show you two ways to get there. Master this, and you’ll be ready for more advanced combinatorics challenges!

📚 *Who’s This For?*
Math and combinatorics enthusiasts
Students prepping for quant interviews
Anyone practicing for math competitions

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