# 2008 AMC 8 Problems/Problem 3

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## Problem

If February is a month that contains Friday the $13^{\text{th}}$, what day of the week is February 1?

$\textbf{(A)}\ \text{Sunday} \qquad \textbf{(B)}\ \text{Monday} \qquad \textbf{(C)}\ \text{Wednesday} \qquad \textbf{(D)}\ \text{Thursday}\qquad \textbf{(E)}\ \text{Saturday}$

## Solution

We can go backwards by days, but we can also backwards by weeks. If we go backwards by weeks, we see that February 6 is a Friday. If we now go backwards by days, February 1 is a $\boxed{\textbf{(A)}\ \text{Sunday}}$

## Solution 2

Since the days of the week repeat every 7 days and $1-13\equiv2\pmod7$, the day of the week of the day 2 days after February 13 is the same as the day of the week of February 1. Since we know that February 13 is a Friday, the day of the week of the day 2 days after February 13 is a Sunday so we get that February 1 is a $\boxed{\textbf{(A)}\ \text{Sunday}}$.

## Solution 3

We can go back 2 weeks and say that Friday is the -1st of February. Going forward 2 days, we get that February 1st is Sunday. So our answer is $\boxed{\textbf{(A)}\ \text{Sunday}}$.