Found problems: 4
2000 Harvard-MIT Mathematics Tournament, 25
Find the next number in the sequence $131, 111311, 311321, 1321131211,\cdots$
2012 AMC 10, 12
A year is a leap year if and only if the year number is divisible by $400$ (such as $2000$) or is divisible by $4$ but not by $100$ (such as $2012$). The $200\text{th}$ anniversary of the birth of novelist Charles Dickens was celebrated on February $7$, $2012$, a Tuesday. On what day of the week was Dickens born?
$ \textbf{(A)}\ \text{Friday}
\qquad\textbf{(B)}\ \text{Saturday}
\qquad\textbf{(C)}\ \text{Sunday}
\qquad\textbf{(D)}\ \text{Monday}
\qquad\textbf{(E)}\ \text{Tuesday}
$
1994 AIME Problems, 14
A beam of light strikes $\overline{BC}$ at point $C$ with angle of incidence $\alpha=19.94^\circ$ and reflects with an equal angle of reflection as shown. The light beam continues its path, reflecting off line segments $\overline{AB}$ and $\overline{BC}$ according to the rule: angle of incidence equals angle of reflection. Given that $\beta=\alpha/10=1.994^\circ$ and $AB=AC,$ determine the number of times the light beam will bounce off the two line segments. Include the first reflection at $C$ in your count.
[asy]
size(250);defaultpen(linewidth(0.7));
real alpha=24, beta=32;
pair B=origin, C=(1,0), A=dir(beta), D=C+0.5*dir(alpha);
pair EE=2*dir(180-alpha), E=intersectionpoint(C--EE, A--B);
pair EEE=reflect(B,A)*EE, EEEE=reflect(C,B)*EEE, F=intersectionpoint(E--EEE, B--C), G=intersectionpoint(F--EEEE, A--B);
draw((1.4,0)--B--1.4*dir(beta));
draw(D--C, linetype("4 4"),EndArrow(5));
draw(C--E, linetype("4 4"),EndArrow(5));
draw(E--F, linetype("4 4"),EndArrow(5));
draw(F--G, linetype("4 4"),EndArrow(5));
markscalefactor=0.01;
draw(anglemark(C,B,A));
draw(anglemark((1.4,0), C,D));
label("$\beta$", 0.07*dir(beta/2), dir(beta/2), fontsize(10));
label("$\alpha$", C+0.07*dir(alpha/2), dir(alpha/2), fontsize(10));
label("$A$", A, dir(90)*dir(A));
label("$B$", B, dir(beta/2+180));
label("$C$", C, S);[/asy]
2012 AMC 12/AHSME, 9
A year is a leap year if and only if the year number is divisible by $400$ (such as $2000$) or is divisible by $4$ but not by $100$ (such as $2012$). The $200\text{th}$ anniversary of the birth of novelist Charles Dickens was celebrated on February $7$, $2012$, a Tuesday. On what day of the week was Dickens born?
$ \textbf{(A)}\ \text{Friday}
\qquad\textbf{(B)}\ \text{Saturday}
\qquad\textbf{(C)}\ \text{Sunday}
\qquad\textbf{(D)}\ \text{Monday}
\qquad\textbf{(E)}\ \text{Tuesday}
$