100÷4=25

B takes it first, so no matter how much medicine B takes.

The sum of the quantity taken by A and that taken by B is equal to 4.

For example:

B takes 2, A takes 2.

B takes 3 and A takes 1.

B takes 1 and A takes 3.

This way, the last one will definitely be taken away by A.

So A must win.