1) Here is the new Montlake state.

x	x	x	o	o	o
x	x	x	o	o	o
x	x	o	o	o	o
o	o	o	o	x	x
o	o	o	x	x	x
o	o	o	x	x	x

Montlake is to be divided into four districts with nine voters in each district. Each district should be connected (so that you can walk from one point in the district to another without stepping outside or across a corner). Each district votes to chooses a single representative, belonging to X or O, that best represents that district according to the majority in that district.


Draw district lines so that:

a) The O's and X's both have two representatives (i.e. in two districs X has a majority, and in two districts O has the majority).
b) The O's have three representatives and the X's have one.
c) The O's have one representative and the X's have three.

Is it possible for the O's to have all four representatives? What about the X's? Why or why not?





2) Euler is out taking a walk. He wants to start at his house, walk along each path once and only once, and then return where he started. A walk like this is called and Euler circuit. Can Euler do an Euler circuit in this neighborhood? What is the route?

Later Euler moves into a new neighborhood. Can he do an Euler circuit in this neighborhood?