[Math] What time does a 12-hour clock read:

discrete mathematicsmodular arithmeticnumber theory

What time does a 12-hour clock read

a) 80 hours after it reads 11:00?

b) 40 hours before it reads 12:00?

c) 100 hours after it reads 6:00?

The solution

a. (11 + 80) mod 12 = 7

b. (12 + 40) mod 12 = 4

c. (100+ 6) mod 12 = 10

How can I calculate to get 7 for a?

Edit I figured it out that they use the remainder right?

Best Answer

In non-modular arithmetic language:

After 12 hours, clock reaches back to 11. So we find number of "12" hours in 80 hours =$6\times12=72$

There's remaining $8$hours which pushes clock handle from 11 to 7 (11,12,1,2,....,7)

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