Either the answer is even in every possible world, or it is odd in every possible world. It can't be legitimate to consider worlds where it is even and worlds where it is odd, as if they both actually existed.

If you don't know which is the case, considering such possibly impossible possible worlds is a standard tool. When you're making a decision, all possible decisions except the actual one are actually impossible, but you still have to consider those possibilities, and infer their morally relevant high-level properties, in the course of coming to a decision. See, for example, Controlling Constant Programs.