Idealogian

Brain Teaser - Even-handed Clock

I just heard this one from my sister and brother-and-law, though the "back story" is my own invention.

A disgruntled watchmaker, having just been informed that he is about to be downsized, has thrown a little mischief into the works. His final watch was produced with minute and hour hands that are exactly the same length. (There is no second hand.) Otherwise, however, the watch is perfectly precise.

His employers, having noticed the problem, have no choice but to sell the watch at a steep discount. In order to determine the discount, they must first answer the question: how many times a day is the watch truly ambiguous? Obviously, one could watch the watch for a minute and see which hand moves more, thereby determining which hand is which and thus the correct time. But how many times a day will a single glance at the watch (and perhaps a bit of brainpower) leave the wearer absolutely unable to determine the correct time?

Oh, and chag samei'ach!