What is the time 6 hours after 10 o clock at ni... - SS1 Mathematics Modular Arithmetic Question
What is the time \(6\ hours\) after \(10\ o’clock\) at night (\(10:00\ pm\))?
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Assuming a 12-hour clock, that is modulo 12
\(6\ \oplus 10\ (mod\ 12)\ \ \ \ \ = 16\ (mod\ 12)\ \ \ \ \ \ = \ \frac{16}{12}\ = 1\ remainder\ \mathbf{4}\)
Thus, \(6 \oplus 10\ (mod\ 12)\ \equiv \mathbf{4}\), meaning the time will be 4 o’clock or 4:00 am the next day.
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