Discrete Mathematics with Applications 4th Edition

Published by Cengage Learning
ISBN 10: 0-49539-132-8
ISBN 13: 978-0-49539-132-6

Chapter 4 - Elementary Number Theory and Methods of Proof - Exercise Set 4.4 - Page 189: 14

Answer

Monday

Work Step by Step

The formula for the day of the week in $N$ days is $DayN = ((DayT)+N)\ mod\ 7$, where $DayN$ is the day of the week in $N$ days, $DayT$ is the day of the week today, and the days Sunday through Saturday are numbered $0$ through $6$, respectively. Therefore, if $DayT=2$ and $N=1000$, we have $DayN = (2+1000)\ mod\ 7=1002\ mod\ 7=1$, because $1002=7(143)+1$. See example 4.4.3 for an explanation of the formula $DayN = ((DayT)+N)\ mod\ 7$.
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