Expii is wishing you a great start of a new school year! Have you solved all the problems in Solve set 40?
Here’s Problem 5:
Welcome to the 2016-2017 school year! A brand new school has installed exactly 2017 lockers, numbered from 1 to 2017, running side by side all the way around its perimeter so that locker #2017 is right next to locker #1. After checking the lockers, all of the odd numbered ones were left open, and all of the even numbered ones were shut. A prankster starts at locker #1, and flips its state from open to shut. He then moves one locker to the left (to #2017), and flips its state from open to shut. He then moves three more lockers to the left (to #2014), and flips its state from shut to open. He then moves five more lockers to the left (to #2009), and flips its state from open to shut. He keeps going in this way, until he has flipped a total of 2017 lockers. How many lockers are open after he is finished?
Check out Top Solver Lindsay Hans’ top-voted explanation for some help!