This month’s brainteaser is very conceptual and therefore does NOT require much time. Give it a try!
You leave Atlanta at 8am on Sunday morning and arrive in Detroit at 8pm that same day. You take breaks on the 12 hour journey and you change speeds throughout the trip due to traffic, weather, and fatigue. The next Sunday you leave Detroit at 8am and return home to Atlanta at 8pm that night traveling along the exact same route (and again taking breaks and changing speeds along the way).
Is it possible that you are never at the exact same location at the exact same time on the two Sundays? If so, how? If not, why not?
Answer:
No, it’s not possible to construct 2 drives such that you are never at the same location at the same time on the two consecutive Sundays. The easiest way to prove this is to imagine that 2 different people are leaving from the 2 locations at 8am on the same day (one driving from Atlanta to Detroit and the other from Detroit to Atlanta). If the two people both arrive at the opposite city at 8pm, then they must have crossed paths at a certain time. The same would be true if you superimpose the two paths that you traveled on top of each other. There would be a location somewhere along the route where the two cars (you on the first Sunday and you on the second Sunday) would have to meet.