It is well known that a stopped clock gives the exact time twice a day, while a clock that gains or loses time may not be right more than once over a period of months.
My clever father adjusted his clock to give the correct time at least twice a day, while running at the normal rate.
Assuming he was not able to set it perfectly (a reasonable assumption) how did he do it?
My initial thought was to run the clock backwards, but I believe that this violates the intent of the wording that the clock was running at the normal rate. (to me, the word rate implies a vector-like measurement, which would include the direction.)
My next thought was similar to the Charlies post where some harmonic error was added in to the timing mechanism, causing the clock to alternately be ahead or behind the actual time, but always close. I discarded this as, while my own father is very clever, he is not a watchsmith and cannot make these adjustments, therefore I assume that "your" father then also cannot.
Obviously the stopped clock works to show the exact time twice per day, but this also seems to me to be in violation of the "rules" regardless of how the clock comes to not be moving.
So, my last thought seemed to be the only one that fits, however, it only works on clocks without labelling. Flip it over, lay it on its side, or otherwise rotate the face some amount from the standard vertical. This doesnt work on its own (the hour would always be incorrect), however in combination with pre-setting the clock to be off by some amount or switching the hour and minute hands, may allow the clock to show the actual true time twice or more per day. This is as far as I go thought, as testing this theory seems to much like work. And f the face is labelled with 1-12, then this method fails as well, as the clock clock reader would then be able to "correctly" orient their angle of viewing.
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