36 University

ACT test prep
that actually works


The Locker Problem – January 2017 Challenge

act-math-locker-pic1Number 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:

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 included, and post as a reply to any of our Locker Problem social media posts or send to lockerchallenge@36university.com. Submissions must be posted by midnight eastern time on January 31st. Impress us with your approach to solving this problem!


act-math-lockergiveawaypic2What 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

$15 Starbucks gift card


How Will 36U Choose a Winner?

At 36U, we value simple, precise solutions. We will draw a winner on February 1st from among entries with correct answers and easy-to-understand explanations. (or: whose solutions are correct and whose approach is easily understood.)


More 36U Resources:

36U Blog Posts

36U ACT Tips

36U ACT Prep Program