We hope you realized that lockers are only touched by students who are factors of that locker number, i.e. Here’s the question: “Which lockers are left open after all 100 students have walked the row of lockers?”Īs many of you found, the perfect square lockers (#s 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100) are the only lockers left open. That same pattern continues for all 100 students. The 5 th student changes every 5 th locker. The 4 th student changes every fourth locker. The 3 rd student changes every 3 rd locker if it’s closed, she opens it if it’s open, she closes it. The second student closes every 2 nd locker. Imagine 100 lockers numbered 1 to 100 with 100 students lined up in front of those 100 lockers: We hope you enjoyed and learned from the problem.įor those who missed it, here was the challenge problem: We want thank all who attempted the January 2017 Math Challenge.
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