Difference between revisions of "2021 AMC 12B Problems/Problem 15"

Line 1: Line 1:
Please do not write here before the contest has occurred.
+
==Problem 15==
 +
The number <math>2021</math> is expressed in the form <cmath>2021=\frac{a_1!a_2!...a_m!}{b_1!b_2!...b_n!},</cmath> where <math>a_1 \geq a_2 \geq \cdots \geq a_m</math> and <math>b_1 \geq b_2 \geq \cdots \geq b_n</math> are positive integers and <math>a_1+b_1</math> is as small as possible. What is <math>|a_1 - b_1|</math>? <math>\textbf{(A)}\ 1 \qquad \textbf{(B)}\ 2 \qquad \textbf{(C)}\ 3 \qquad \textbf{(D)}\ 4 \qquad \textbf{(E)}\ 5</math>

Revision as of 18:34, 11 February 2021

Problem 15

The number $2021$ is expressed in the form \[2021=\frac{a_1!a_2!...a_m!}{b_1!b_2!...b_n!},\] where $a_1 \geq a_2 \geq \cdots \geq a_m$ and $b_1 \geq b_2 \geq \cdots \geq b_n$ are positive integers and $a_1+b_1$ is as small as possible. What is $|a_1 - b_1|$? $\textbf{(A)}\ 1 \qquad \textbf{(B)}\ 2 \qquad \textbf{(C)}\ 3 \qquad \textbf{(D)}\ 4 \qquad \textbf{(E)}\ 5$

Invalid username
Login to AoPS