seven+bridges+Problem

The northern bank of the river is occupied by the castle of the Blue Prince; the southern by that of the Red Prince. The east bank is home to the Bishop's church; and on the small island in the center is a tavern.

It is understood that the problems to follow should be taken in order, and begin with a statement of the original problem:

It being customary among the townsmen, after some hours in the tavern, to attempt to **walk the bridges**, many have returned for more refreshment claiming success. However, none have been able to repeat the feat by the light of day.
 * The Eighth Bridge:** The Blue Prince, having analyzed the town's bridge system by means of graph theory, concludes that the bridges cannot be walked. He contrives a stealthy plan to build an eighth bridge so that he can begin in the evening at his castle, walk the bridges, and end at the tavern to brag of his victory. Of course, he wants the Red Prince to be unable to duplicate the feat from the Red Castle. //Where does the Blue Prince build the eighth bridge? (you can answer in the form of a labeled drawing)//
 * The Ninth Bridge****:** The Red Prince, infuriated by his brother's legendary solution to the problem, wants to build a ninth bridge, enabling //him// to begin at his castle, walk the bridges, and end at the tavern to rub dirt in his brother's face. As an extra bit of revenge, his brother should then no longer be able to walk the bridges starting at his castle and ending at the tavern as before. //Where does the Red Prince build the ninth bridge?// //(you can answer by adding to your drawing. Be sure to labeled drawing)//
 * The Tenth Bridge****:** The Bishop has watched this furious bridge-building with dismay. It upsets the town's P.R. and, worse, contributes to excessive drunkenness. He wants to build a tenth bridge that allows //all// the inhabitants to walk the bridges and return to their own beds. //Where does the Bishop build the tenth bridge? (again, answer by adding to you drawing)//