"The Yellow Path Dilemma: Can You Cross Without Repeating?"

"The Yellow Path Dilemma: Can You Cross Without Repeating?"

To pass through the yellow pathway shown in the image (which resembles a peace symbol) without crossing the same segment twice, we can think of the problem as one in graph theory, specifically an Eulerian path problem.

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🔍 Problem Summary:

The shape consists of:

• A circle with three inner lines (rays) connecting at the center and touching the circle at three points.

• The possible paths are the yellow segments (lines), so there are a total of 6 segments.

To go through all segments exactly once without repetition, a basic rule from Euler's graph theory must apply:

📌 A graph has an Eulerian path (a path that visits every edge exactly once) if and only if:

• Exactly two vertices have an odd degree (odd number of connections), and all other vertices have an even degree.

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🧠 Shape Analysis:

Vertices in this case are:

1. The center, which connects to 3 segments (the rays)

2. The 3 outer points on the circle, each connected to 2 segments (a ray and a curve segment)

✔️ The center has degree 3 (odd)

✔️ Each outer point has degree 2 (even)

⛔ So only one vertex has an odd degree ➤ this does not satisfy the Eulerian path conditions.

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📌 Conclusion:

It is not possible to pass through all yellow lines exactly once without crossing the same point twice, unless:

• The structure is changed or

• The rules (e.g., starting/ending at specific points) are relaxed.