In article <email@example.com>, <firstname.lastname@example.org> writes: NTP-Posting-Host: crchmf73.rich.bnr.ca > > Assume an analog watch with three arms for: hours, minutes, > and seconds, starting at noon hour when they are all three > perfectly lined up. The question is whether will these three > arms be ever lined up again before they reach the noon position. >
No. This is easy to prove using the Chinese remainder Thm.
I have a more interesting question:
Do the three hands ever trisect the face of the clock? If not, how close do they come in terms of minimizing the sum of the squared deviations from 120 degree angles?