Please point to where anything in the problem statement says anything about alkaline batteries. All it says is that they are 1.5V AA batteries.

Correct, and the only commercially available 1.5V AA cells commonly used are either Alkaline (majority of market) or carbon zinc. Ni Cad or NiMh would be 1.25V batteries.

 

I think you have to ignore the charging/discharging issue for this problem.

OK, I was considering how sad I feel that there is a teacher giving students exercises encouraging them to hook up stacks of battery cells that oppose each other in series, but what do I know......

 

As I have said several times, I do not like this problem at all, for a variety of reasons. Just as I do not like problems that through around components with values of 1 ohm, or 1 henry, or 1 farad. I much prefer problems that use realistic scales of component values and that do not foster excessively unrealistic impressions of what components, including batteries can do. But the fact remains that the OP has to deal with a given problem, which is a paper problem, and only has enough information to employ a battery model consisting of an ideal voltage source in series with a fixed resistor. As horrible as the problem is, I think the OP was able to gain some insight into the 'thinking outside the box' for lack of a better description.