The philosopher Immanuel Kant had, let us say, exceptionally regular habits. He particularly liked to have his grandfather clock set at precisely the correct time. One day he was distressed to find the clock had run down. Evidently his servant had forgotten to wind it. Kant couldn’t reset the hands because, as his watch was at the repair shop, he didn’t know the correct time.
That evening he walked to the house of his friend Meyer, a mile or so away, for their weekly chess game. Kant always walked at the same steady pace, though he had never taken note of the time of this particular walk took. He glanced at the clock in Meyer’s hallway when he arrived, played several games of chess, checked the clock again, and then returned home, taking the same route by which he had come. When he arrived home, he immediately set his grandfather clock correctly. How did he do it?
Solution
Kant started his clock running before leaving for Meyer’s house though, of course, it was showing the wrong time. When he returned, however, it told him how long he had been away. From this elapsed time, he subtracted the time spent at Meyer’s which he knew from looking at Meyer’s clock upon arrival and departure. This gave him the amount of time he had spent walking to and from Meyer’s. He took half of that to get the time for walking one way between his house and Meyer’s. Adding this time to the time on Meyer’s clock observed upon leaving gave him the time at which he arrived home. He could now set his clock to this time plus the few minutes that had elapsed whilst figuring this all out. All of this assumes that Meyer's clock was correct.