Established research on pair programming reveals benefits, including increasing communication, creativity, self-efficacy, and promoting gender inclusivity. However, research has reported limitations such as finding a compatible partner, scheduling sessions between partners, and resistance to pairing. Further, pairings can be affected by predispositions to negative stereotypes. These problems can be addressed by replacing one human member of the pair with a conversational agent. To investigate the design space of such a conversational agent, we conducted a controlled remote pair programming study. Our analysis found various creative problem-solving strategies and differences in conversational styles. We further analyzed the transferable strategies from human-human collaboration to human-agent collaboration by conducting a Wizard of Oz study. The findings from the two studies helped us gain insights regarding design of a programmer conversational agent. We make recommendations for researchers and practitioners for designing pair programming conversational agent tools.