There is a hint in the book.
For p2/p1 <=1 /2, consumer 1 chooses only good 2; for 1/2 < p2/p1 <2, the choice is the same amount of good 1 and 2; and for 2 <= p2/p1 only good 1 is chosen.
I suggest you draw a diagram for consumer 1, pick an arbitrary endowment point and work out what happens as a budget line through this point turns as p2/p1 varies.
For part (a) the answer is {(t,t):0<=t<=1}.
For part (b) I think there is only one point where consumer 1 and 2's choices can coincide and that is (1,0) in consumer 1's coordinates.
I could be wrong though!