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It's a cliché that 'even' a stopped clock is right twice a
but one which is fast or slow is never right.
This is intuitively true, but does it have to be the case?
There are some common changes made to timepieces
that when stopped they show the correct time less than
twice a day
on average - a 24-hour clock (either with the
hour hand going round once a day, or a separate am/pm
indicator) would be right once a day, while a face
the day of the month is right only twice a month at
consider these degenerate cases and won't consider them
But it occurs to me that a very fast clock could be right
three -or more- times a day.
The precision broken clock is a post-manufacture
modification, made solely by adjusting its existing parts.
"three times/day" model this causes the clock to run
exactly two and a half times too fast. One can choose
of the three times a day that the clock is correct simply
setting it at that time (the other two times are at one-
third day intervals).
Suppose one sets the correct time at midnight. The
will then increment by 2œ hours per hour, so that by 8
it will have proceeded through 20 hours; the face will
8 o'clock. At 4 pm it will overtake the true time again,
the cycle will repeat at midnight.
What time is it, Eccles? [Loris, Apr 12 2015]
Here's one for ya...
Spot on every quarter hour. [FlyingToaster, Apr 12 2015]