, 2013

Problem:
Pick a subset of at least four of the following seven numbers, order them from least to greatest, and write down their labels (corresponding letters from $A$ through $G$) in that order:

$(A)$ $\pi$;

$(B)$ $\sqrt{2}+\sqrt{3}$;

$(C)$ $\sqrt{10}$;

$(D)$ $\frac{355}{113}$;

$(E)$ $16 \tan^{-1} \frac{1}{5} - 4 \tan^{-1} \frac{1}{240}$;

$(F)$ $\ln(23)$;

$(G)$ $2^{\sqrt{e}}$.

If the ordering of the numbers you picked is correct and you picked at least 4 numbers, then your score for this problem will be $(N-2)(N-3)$, where $N$ is the size of your subset; otherwise, your score is $0$.