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.
🔍 Problem Summary:
The shape consists of:
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A circle with three inner lines (rays) connecting at the center and touching the circle at three points.
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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:
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Exactly two vertices have an odd degree (odd number of connections), and all other vertices have an even degree.
🧠 Shape Analysis:
Vertices in this case are:
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The center, which connects to 3 segments (the rays)
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The 3 outer points on the circle, each connected to 2 segments (a ray and a curve segment)
⛔ So only one vertex has an odd degree ➤ this does not satisfy the Eulerian path conditions.
📌 Conclusion:
It is not possible to pass through all yellow lines exactly once without crossing the same point twice, unless:
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The structure is changed or
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The rules (e.g., starting/ending at specific points) are relaxed.
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