Two old problems

Problem 1: There are six regiments, each having six officers, one of each of six possible ranks. Without looking at every single possible combination (poor, poor Tarry), can you work out if is it possible to parade these thirty six officers in a six by six pattern, so that every row and and every column contain exactly one officer of each rank and exactly one member of each regiment?

Problem 2: Given a set of boys and a set of girls, each girl knowing a specified set of boys, show that it is possible for all girls to marry boys they know if and only if* any set of k girls know altogether at least k boys.

*if and only if: show that both LHS=>RHS and LHS