A Priestly Poser
Holmes and I once tackled a case that involved the disappearance of a priest, and at one point our investigations brought us to a remote hilltop chapel.
“Watson,” Holmes said, as we began our ascent up the broad stone steps, “consider this. A priest sets off at nine a.m. up a path to a hilltop chapel, and arrives at nine p.m. The following day, he sets off at nine a.m., and reaches the bottom at nine p.m. Is there any moment on the second day at which he is at exactly the same step on the path at exactly the same time as he was on the previous day?”
I frowned. “Surely that depends on his speed, and whether he took breaks at any point on either day,” I answered. “How can you possibly know the answer without more information?”
“Know?” he replied. “I can do one better. I can prove it.”
What was Holmes’ proof?