And if the French Revolution's audacious idea of decimal time (1d=10h, 1h=100m, 1m=100s) had stood the test of, uh, time -- then every time the hour and minute hand coincided, the second hand would be there too. (The "11" and "708" become "9" and "990", and every exact ninth is also an exact 990th.)

The even more interesting question is, given X hours per day (or per half-day, if that's what your clock-face measures) and Y minutes per hour, how many triple alignments are there as a function of X and Y?

Peter