Answer
See explanation.
Work Step by Step
Bulb A has the largest voltage drop across it, $\epsilon$, while bulb B and bulb C have a voltage drop of $\frac{\epsilon}{2}$ each.
As a result of bulb A having the greatest potential difference across it, it is the brightest, and has the most current flowing through it.
If bulb A is unscrewed, the voltage across the other branch stays the same, so bulbs B and C stay lit in their dimmer state.
If bulb B is unscrewed, this cuts the current to bulb C, so both bulbs are out. The voltage across the other branch stays the same, so bulb A stays lit.
If bulb C is unscrewed, this cuts the current to bulb B, so both bulbs are out. The voltage across the other branch stays the same, so bulb A stays lit.
