combinatorics question

golden

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Mar 10, 2016
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There is a 3*3*3 cube block, starting at the corner, you are allowed to take 1 block each time, and the next one must share a face with the last one. Can it be finished in the center?
This is a question about graph theory( i think), and obviously it is impossible to finished in the center. I start to consider about the Hamiltonian path and the degree of each vertex , but it is different because you have to start and end with a specific vertex. Can anyone tell me the reason why is it impossible?
 
So in task we have to find a way going through whole cube with no crosses? One block can be touched once?
 
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