  Currently there are several approaches to resolution of singularities in
positive characteristic all of which have hit some obstruction. One natural
idea is to try to construct new meaningful examples at this point to gain a
wider range of experience. To produce such examples we mimic the characteristic
zero approach and focus on cases where it fails. In particular, this short note
deals with an example-driven study of failure of maximal contact and the search
for an appropriate replacement.
