
The solution
comes from
Subj:.....A
Clock Puzzle (S486, S601)
From the book
"Mathematical Puzzles of Sam Loyd"
Edited by Martin Gardner
From: Dover Publications in 1959
If the minute hands
goes twelve times faster than the hour
hand, then they will
meet eleven times during every 12hour
period. By
taking the eleventh part of 12 hours for our
constant, we find
there will be a meeting of hands every
65 and 5/11 minutes,
or every 65 minutes, 27 and 3/11
seconds. The
hands will next come together, therefore, at
5 minutes, 27 and
3/11 seconds past 1 o'clock. 