Why do clocks measure the hours in sets of 12, repeating the numbers after 12 hours? And why minutes and seconds are grouped in sets of 60? Well, mostly by convenience and historical reasons, but mathematically we could make clocks whose hands make a full turn every 3 hours, or 4 hours, or any number of hours we wish, and likewise with the minutes and seconds.

Would we have the same information as with our usual 12-hours and 60-minutes clocks? Could we translate from one to another?

Discover the Chinese Remainder Clock and its surprising arithmetic properties.