Number Theory

Basic Applications of Modular Arithmetic

Practical Applications of Modular Arithmetic Warmup


If you start watching a 57-minute-long episode of a TV show at 8:42 pm, what time will it be when the episode is over?

If your birthday is on a Monday this year and neither this year nor the next year is a leap year, what day of the week will your birthday be on next year?

On the first day of class, a teacher writes her name on the board in a secret code:


What is the actual last letter of her last name?

If the local time in Tokyo is 16 hours ahead of the local time in San Francisco, and you take a 10-hour flight from Tokyo to San Francisco that leaves Tokyo at 2 pm Tokyo time, what time will it be in San Francisco when you land?

If you go 38 hours without sleeping starting at 8 am, and then you sleep for the next 11 hours, what time will it be when you wake up?


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