A competent logician is walking down an unfamiliar road to reach his home, until he reaches a fork. Stood by each of the routes is a twin, who both look identical to each other. He has been warned of these twins by a passerby: one of them always tells the truth, and the other always lies.
Being a competent logician, he asks a single question of one of the brothers to find the correct route home. Out of curiosity he continues to ask questions until he discovers which of the twins lies and which one tells the truth.
In asking his questions, the logician discovers that these twins, whilst mystically cursed to only ever address the truth from a single perspective, have been given the ability to speak the truth or lie about everything, even if they have no knowledge of the subject.
The logician gets excited by this, and considering that he is not in a rush as he has no further plans for that day, and he knows his cat at home can fend for itself for a while, he spends the next several hours interrogating the twin that tells the truth, occasionally clarifying with his brother, by constructing a series of carefully phrased yes/no questions.
He learns the answers to some of life's greatest questions in subjects he previously had no idea about, such as quantum physics, religion and philosophy. He also discovers a great many interesting secrets about his friends and family, and also learns facts that would help him to impress the person that he has a crush on.
This is until the logician reaches a stumbling block. He asks the truth teller a question that seems straightforward, but upon asking the twin the same question, he observes that he gives an answer that is the same as his brother's answer. Confused, he attempts ask the same question again, and finds that the twins again seem to agree on a single result.
The logician reasons to himself:
Logically, this should be impossible. As both twins separately know exactly what the truth is, if one of them always lies and the other always tells the truth, then they should never appear to be in agreement on the answer to a particular question.
He fears that his skills for reasoning and logic have become a poisoned chalice, as he can no longer trust any of the things that he has been told by either of the twins.
Disheartened, the logician believes he has been swindled by the passerby that gave him the warning about these twins, and feels that he has wasted an entire day. Despite everything earlier appearing to make sense to him, he decides that the information he has learned is useless, and promptly forgets everything he was told that day, before walking the rest of the journey home.
What question could the logician have asked?