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Basic Applications of Modular Arithmetic

Solve integer equations, determine remainders of powers, and much more with the power 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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