MathDB
Clerks sorting files

Source: AIME II 2013, Problem 7

April 4, 2013
modular arithmeticAMCnumber theoryalgebraAIME

Problem Statement

A group of clerks is assigned the task of sorting 17751775 files. Each clerk sorts at a constant rate of 3030 files per hour. At the end of the first hour, some of the clerks are reassigned to another task; at the end of the second hour, the same number of the remaining clerks are also reassigned to another task, and a similar reassignment occurs at the end of the third hour. The group finishes the sorting in 33 hours and 1010 minutes. Find the number of files sorted during the first one and a half hours of sorting.