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:
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 firstname.lastname@example.org. Submissions must be posted by midnight eastern time on January 31st. Impress us with your approach to solving this problem!
The winner will receive the 36U Winter Care Package:
3 months access to 36U ACT Prep
36U Tee (Long-sleeve)
$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: