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Difference between revisions of "2013 AMC 12B Problems/Problem 15"

(Created page with "==Problem== the number <math>2013</math> is expressed in the form <br \> <center> <math>2013 = \frac {a_1!a_2!...a_m!}{b_1!b_2!...b_n!}</math>,</center><br />where <math>a_1 \ge...")
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Revision as of 14:57, 22 February 2013

Problem

the number $2013$ is expressed in the form

$2013 = \frac {a_1!a_2!...a_m!}{b_1!b_2!...b_n!}$,


where $a_1 \ge a_2 \ge ... \ge a_m$ and $b_1 \ge b_2 \ge ... \ge b_n$ are positive integers and $a_1 + b_1$ is as small as possible. What is $|a_1 - b_1|$?

$\textbf{(A)}\ 1 \qquad \textbf{(B)}\ 2 \qquad \textbf{(C)}\ 3 \qquad \textbf{(D)}\ 4 \qquad \textbf{(E)}\ 5$

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