An ant crawls along the edges of the cube. Will she be able to go around all the edges in sequence, passing over each edge exactly once? Justify the answer.

Solution:

1. Understand the cube:
- A cube is a 3-dimensional solid shape.
- It has 12 edges and 8 vertices.
- Each vertex is connected to 3 other vertices.

2. Use Euler's Theorem for graph theory:
- Euler's Theorem states that a graph has an Eulerian path if it contains exactly 0 or 2 vertices of odd degree.
- In a cube, all vertices have a degree of 3 (as each vertex is connected to 3 edges).

3. Analyze the cube:
- Since all 8 vertices have an odd degree (3), the cube's graph has 8 vertices of odd degree.
- This makes it impossible to have an Eulerian path according to Euler's theorem.

4. Conclusion:
- It is not possible for an ant to traverse every edge of a cube exactly once without retracing steps.

Answer:
- An ant cannot traverse each edge of a cube exactly once.