Puzzle number 51 from Martin Gardner's "My Best Mathematical and Logic Puzzles":
It is said that Immanuel Kant was a bachelor of such regular habits that the good people of Königsberg would adjust their clocks when they saw him stroll past certain landmarks.
One evening, Kant was dismayed to discover that his clock had run down. Evidently his manservant, who had taken the day off, had forgotten to wind it. The great philosopher did not reset the hands because his watch was being repaired and he had no way of knowing the correct time. He walked to the home of his friend Schmidt, a merchant who lived a mile or so away, glancing at the clock in Schmidt’s hallway as he entered the house.
After visiting Schmidt for several hours Kant left and walked home along the route by which he came. As always, he walked with a slow steady gait that had not varied in 20 years. He had no notion of how long his return trip took. (Schmidt had recently moved into the area and Kant had not yet timed himself on this walk.) Nevertheless, when Kant entered his house, he immediately set his clock correctly.
How did Kant know the correct time?There is one point on which the puzzle could use additional clarification. Assume that the path from Kant's house to Schmidt's house was "flat", so that it took Kant exactly the same amount of time to make the onward and return journeys.