1B, C, F, G (from the textbook) and the mountain climber problem below:

A man and his wife are climbing a piecewise linear mountain from opposite sides as below, but they start off at the same level at the bottom.  As they climb, they wish to go to the summit so that they continuously stay the same height.  Can they do it?  Why? or Why not?

A Java version of the figure below

Suggestion:  Construct horizontal lines through each vertex as above and add vertices at all the intersections.  Then consider the graph G whose vertices are all pairs (x,y) where x is one of the vertices (on the left) for the man, and y is one of the vertices at the same height for the wife (on the right).  Connect two vertices by an edge if the man and wife can move together between adjacent levels staying on the mountain and staying together at the same height.  The problem is then to show that the vertex corresponding to the starting position, where they are both on the bottom, is connected in G to the vertex corresponding to where they are both at the summit.