Done, but raised big question in my mind: is demonstrating that using one of two choices leads to a contradiction essentially the same thing as guessing and finding out whether the guess was correct?
If it doesn't then check your premises, there is a contradiction (you missed) which means there were three choices. Ayn Rand... not.
Yes, TallMike, they should work out the same. But doing it all in your head is more challenging, not a source of shame.
I totally agree with Unike that doing it all in your head is more challenging. But what if the puzzle presents an either/or option with a second independent either/or option that must also be dealt with? Is there a limit to how far ahead you can see without actually determining the outcome of at least one, and maybe two or three, of the possible choices? Can guessing actually be a legitimate and necessary process of elimination, without which there is no logical path to a solution?