Question

Four cities are connected by roads as shown. In how many ways can you start at a city and come back to it without travelling the same road more than once?

• A. 1
• B. 2
• C. 3
• D. 4

Hint:

Trace all unique closed loops without edge repetition — this is a cycle count in graph theory.

Answer 1

The Correct Option is B

The figure forms a graph with 4 nodes and edges like a triangle with a center connected to all corners — total 6 edges.
We are asked: in how many distinct cycles (closed loops) can we go from a city and come back to it, without repeating any edge?
We need to count simple cycles: - Triangle 1: between 3 outer cities (e.g., bottom-left → bottom-right → top → back) - Triangle 2: any two outer cities + the center You can manually trace cycles: 1. Outer triangle: 3 outer cities form 1 triangle (Cycle 1) 2. Inner triangle (e.g., bottom-left → center → bottom-right → back): forms Cycle 2 Only these 2 edge-disjoint cycles exist. \[ \boxed{2} \]