# Problem #871

 871 In year $N$, the $300$th day of the year is a Tuesday. In year $N+1$, the $200$th day is also a Tuesday. On what day of the week did the $100$th day of year $N-1$ occur? $\textbf {(A)}\ \text{Thursday} \qquad \textbf {(B)}\ \text{Friday}\qquad \textbf {(C)}\ \text{Saturday}\qquad \textbf {(D)}\ \text{Sunday}\qquad \textbf {(E)}\ \text{Monday}$ This problem is copyrighted by the American Mathematics Competitions.
Note: you aren't logged in. If you log in, we'll keep a record of which problems you've solved.

• Reduce fractions to lowest terms and enter in the form 7/9.
• Numbers involving pi should be written as 7pi or 7pi/3 as appropriate.
• Square roots should be written as sqrt(3), 5sqrt(5), sqrt(3)/2, or 7sqrt(2)/3 as appropriate.
• Exponents should be entered in the form 10^10.
• If the problem is multiple choice, enter the appropriate (capital) letter.
• Enter points with parentheses, like so: (4,5)
• Complex numbers should be entered in rectangular form unless otherwise specified, like so: 3+4i. If there is no real component, enter only the imaginary component (i.e. 2i, NOT 0+2i).