Possible Increasing Paths in Cubes

Given a cube, a valid label is one where each edge is labeled a distinct number from 1 to 12. An increasing path is a path formed by the edges labeled i,ji, j and kk such that i<j<ki < j < k and the edges i,ji, j and kk form a continuous curve (i.e. edge jj has a common vertex with edges ii and kk, and these 3 edges do not share a common vertex). Over all possible valid labels, what is the minimum number of increasing paths?

×

Problem Loading...

Note Loading...

Set Loading...