1 Four friends, Amir (A), Bex (B), Cerys (C) and Duncan (D), are visiting a bird sanctuary. They have decided that they each will sponsor a different bird. The sanctuary is looking for sponsors for a kite \(( K )\), a lark \(( L )\), a moorhen \(( M )\), a nightjar \(( N )\), and an owl \(( O )\). Amir wants to sponsor the kite, the nightjar or the owl; Bex wants to sponsor the lark, the moorhen or the owl; Cerys wants to sponsor the kite, the lark or the owl; and Duncan wants to sponsor either the lark or the owl.

1. Draw a bipartite graph to show which friend wants to sponsor which birds. Amir chooses to sponsor the kite and Bex chooses the lark. Cerys then chooses the owl and Duncan is left with no bird that he wants.
2. Write down the shortest possible alternating path starting from the nightjar, and hence write down one way in which all four friends could have chosen birds that they wanted to sponsor.
3. List a way in which all four friends could have chosen birds they wanted to sponsor, with the owl not being chosen.