A monk starts up a mountain path at dawn and reaches the top by evening

Why

Anaya is picturing the two walks as separate and unrelated, so a shared point seems like it would take luck. The trick is to imagine both walks happening on the SAME day: one monk starting at the bottom at dawn and walking up, another starting at the top at the same dawn and walking down, along the same path. Those two are on one narrow path heading towards each other, so they MUST pass each other somewhere — and that meeting is a particular place on the path at a particular time of day. That is exactly the spot where the real monk was at that time while going up on day one and while coming down on day two. Test: it does not matter how fast or slowly he walks, whether he stops to rest, or even doubles back for a while — two people walking the same path in opposite directions on the same clock always cross. Her friend is right: there is guaranteed to be one point he passes at the identical time of day on both trips, even though you cannot say in advance where it is.