The three things necessary for a change in character to be believable are the following:
-It’s slow (gradual).
-It’s not linear.
-It’s complete.
A change arc in a character has to have a setup, a reaction and a counter-reaction/conclusion; these stages are gradual and end with a more round character, in a conclusive way that is satisfactory in the sense that the change was complete.
In the text ransom of red chief Bill and Sam needed a hideout to keep red chief away from the town to kidnap him, although if your wanting the answer based on the movie it's because they bought the mine and found out it was worthless, so they used it as a hiding spot to keep red chief.
The correct answer is three ways. An author can draw a character in one of three ways. Direct and indirect characterization may be included in this as well in order for the author to be able to develop its characters in context form.