Friday, September 16, 2011

Kant's Clock

A famous old puzzle.

It is said that Immanuel Kant was a bachelor of such regular habits hat the people in his town would adjust their clocks when they saw him strolling past certain landmarks.

One evening Kant was dismayed to discover that his clock had run down.  Evidently, his servant had forgotten to wind it.  The  great philosopher did not reset his 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 twenty years. He had no notion how long this trip took. Nevertheless, when Kant entered his house, he immediately set his clock correctly.

How did Kant know the correct time?

Top image by faungg, distributed under the CCL.

Answer ideas accepted any time until midnight on Saturday September 17th (EST), on our Family Puzzle Marathon. They will be hidden till then and everyone who submitted a valid solution will get a puzzle point.


Ilya said...

The problem states that Kant's didn't set the hands of his clock, but he must have wound it anyway and took note of the time TK1 when he left for his friend's house. When he arrived at his friends's he took note of the time there - TS1; then when he was leaving he looked at Schmidt's clock again and noted it showed TS2, which allowed him to calculate the time of his stay (TS2-TS1). When he arrived home, he saw the time on his clock was TK2, which meant his total absence was (TK2-TK1). Therefore, the round-trip to Schmidt's house took (TK2-TK1)-(TS2-TS1) and the return trip is half of that. Since he knew he started on his way back at time TS2, he set his home clock to TS2+((TK2-TK1)-(TS2-TS1))/2.

anne-marie said...
It was already the evening when he left home so he probably used the big dipper or the moon.
To have the exact time, maybe his friend gave him a watch.

anne-marie said...

He could also use the formula v=d/t v being constant in this case and d being one mile then add the result to the time he saw before living his friend's house.

TracyZ said...

Solution1: On his way home from Schmidt's house, Kant stopped by the watch repairman and picked up his repaired watch. Since the watch was fixed, and set to the correct time, he used the time on the watch to set the clock at his house upon returning home.

Solution2: On his way home from Schmidt's house, Kant went by a number of landmarks, and as he did so, he saw the clocks that other people in the town had set (based on his walking speed and habits). At the landmark closest to his house, he noted the current time (T1) on a clock in the town (asking a fellow citizen for the time if necessary). He also knew the time it took him to travel from that nearest landmark to his house (L1). When he got home, he set the time on his own clock to T1 + L1.

Kant has walked at the same speed for many years, and his servant and others in town know how long it takes him to walk from his house to his good friend Schmidt's house (L2) and for him to walk from Schmidt's house to his own (L3) (even with a slow and steady gait, it seems as though L2 and L3 could possibly be different if there is a large hill on the path between them). On the day in question, Kant visited his friend Schmidt for many hours. When he entered Schmidt's house he saw that the time on the clock was time T1. After his visit, when he was leaving Schmidt's house, he saw that the clock now showed time T2. Upon arriving home, he asked the servant for L2, and then was able to set his clock as T2 + L3.

Maria said...

I think all the answers are valid but the intended one and the most complete is from Ilya. Kant probably set his clock to a random time before living the house and then used relative times passed on his clock and his friend's clock to figure out how long he walked and the exact time of his return.

anne-marie's solution of telling time by the sun and moon is very creative but then why do we need to mention the friend?

TracyZ came very close to the answer in her Solution3 and therefore I think we should award her a puzzle point along Ilya.

I see that Ilya just reached his 10th puzzle point and it means that he will be wrapped into a puzzle next Friday.

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