36 University

ACT test prep
that actually works


The Locker Problem – January 2017 Challenge

Number properties are rarely reviewed, but they are sometimes tested on the ACT. So, we’ve decided to share a fun, straightforward, and hopefully enlightening item that will have you thinking about number properties. Here’s your January 2017 ACT Math Challenge:

[Insert video]

Imagine 100 lockers numbered 1 to 100 with 100 students lined up in front of those 100 lockers. The first student opens every locker. The second student closes every 2nd locker. The 3rd student changes every 3rd locker; if it’s closed, she opens it; if it’s open, she closes it. The 4th student changes every fourth locker. The 5th student changes every 5th locker. That same pattern continues for all 100 students. Here’s the question: “Which lockers are left open after all 100 students have walked the row of lockers?”.


How Do I Enter?

Take a pic of your solution, with your work and/or explanation included, and post as a reply to any of our Locker Problem social media posts. If you prefer, you can send your response via email to kshipley@36university.com. Submissions must be posted by midnight eastern time on January 31st. Impress us with your approach to solving this problem!


What Will I Win?

The winner will receive the 36U Winter Care Package:

3 months access to 36U ACT Prep

36U Tee (Long-sleeve)

36U toboggan

$10 Starbucks gift card


How Will You Choose a Winner?

At 36U, we value simple, precise solutions. We will draw a winner on February 1st from among the list of entries whose solutions are correct and whose approach is easily understood.