It's 9 o'clock. What time is it in seven hours?
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Clock arithmetic is modular arithmetic wearing a friendly face. On a twelve-hour clock, 9 + 7 is 4, because the numbers wrap around. That is not a quirk of clocks — it is a whole branch of number theory, and it underpins everything from calendars to cryptography.
The days-of-the-week variant is the practical one. Working out what day a date falls on is the same wrap-around calculation, just with a modulus of seven instead of twelve.
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The remainder after division. 16 modulo 12 is 4, which is exactly why four hours after twelve o'clock the clock reads four.
Calendars, musical scales, check digits on card numbers and barcodes, and most modern cryptography. Wrap-around arithmetic is everywhere once you notice it.
Slightly, because the wrap point is less familiar, but the method is identical.