February 3–February 9, 2009

Problem

At a high school, the lockers are in a long rectangular array, with 3 rows of N lockers each, where N is between 400 and 450. Originally, the lockers on the top row were numbered 1 to N, the middle row numbered from N + 1 to 2N, and the bottom row 2N+1 to 3N, all from left to right.

However, one evening the administration changed around the locker numbers so that the first column on the left is now numbered 1 to 3, the second column 4 to 6, and so forth, all from top to bottom.

Three friends, whose lockers are located one in each row, came in the next morning to discover that each of them now has the locker number that used to belong to one of the others.

What are their locker numbers, assuming that they all are three-digit numbers?

Solution

here

List of solvers

Michael Draper (undergrad); Koopa Koo, Dustin Moody, Jacob Lewis (graduate); Gary M. Raymond (staff); Luan Nguyen, Hai Bin Chang, Elizabeth McCranie, Adam Welly, Justin Shih, Steve Wilmarth, Lloyd Sakazaki (outside)

Elizabeth McCranie wins the prize!