Puzzling Travels of a Tom-Cat.
Here's a puzzle I came across recently. I've changed the context to stop people googling the answer :-
A big ginger tom-cat leaves his home at 8:00 one morning and goes trundling around the neighbourhood, pausing here and there to 'leave his calling-card', stopping for a brief nap or two in a particularly warm spot, walking along fences, running through unfriendly gardens (woof woof) and finding a warm car bonnet in a garage at 6:00 in the evening for a rest. Unfortunately, the owner shuts the garage door and the cat is trapped for the night.
At 8:00 the next morning the garage door opens and the cat comes scooting out. Over the course of the day he takes the exact same path he took the day before but in reverse. He stops in different places, makes his mark in other places and takes his naps at different places along the way, arriving back at his own house at 6:00 in the evening for a well deserved meal.
The question :-
What is the likelihood that there will be a time and place along the route where he is at EXACTLY the same point on the route at EXACTLY the same time of day on both days?