Question Status
- This question is open for discussion
Similar Questions
Question: A Calculus I Question
- Posted By: steven
- Subject: Mathematics
- Report? Flag for Abuse
A Calculus I Question
How do I do this ?? Decompose a cube into 27 smaller cubes as follows: A termite is to travel through all of the smaller cubes exactly once. The termite is only allowed to travel parallel to the faces of the smaller cubes. (Only up, down, left, right) Can you construct a path where the termite goes through each smaller cube exactly once and terminates at the interior cube (the hidden cube).
- Posted By: zeno
- Report? Flag for Abuse
You got this in a Calculus class? This problem is best represented using graph theory. Construct a graph where each vertex is one of the smaller cubes. Then for each vertex/cube draw an edge to each adjoining cubes (i.e. the ones that are up, down, left, and right of that cube). Then you just need a find a path through all of the vertices exactly once and ends at the vertex represented by the vertex representing the center cube (it would be a variant of what is called a Hamiltonian path).