Maths Puzzle: Back to Black
Why Mathematics Stack Exchange recommends it
Mathematics Stack Exchange users link it when someone asks why only square numbers survive in the locker or prison-door problem, since it gives a clear and entertaining visual explanation.
Recommended by 2 people across 2 different months, 2013 to 2017.
What it is
James Grime of singingbanana poses the classic locker puzzle using 90 Othello pieces: flip every second piece, then every third, and so on up to every 90th, and ask which end up black side up. A short, friendly walkthrough shows why the answer is the perfect squares.
What people said
Recommends Pingk · 2013-11 · Mathematics Stack Exchange · on “Prison problem: locking or unlocking every $n$th door for $ n=1,2,3,...$”
This video provides a really wonderful visual explanation for the exact problem you are describing. The video only goes up to 90, but provides all the information you need to generalise it to 100. [this video]
Recommends Cody · 2016-11 · Mathematics Stack Exchange · on “The locker problem - why squares?”
You should check out this video [this video] from mathematician James Grime. He basically repeats the answers below, but his explanation is entertaining.
Cites pavle · 2017-10 · Mathematics Stack Exchange · on “Is there a simple formula for computing this sum?”
I was watching this video from James Grime on his channel singingbanana: [this video] and I wondered how many times does he have to flip every othelo piece. So I found this sum: $$\sum_{k=1}^n \left \lfloor \frac{n}{k} \right \rfloor$$ Is there a way to compute it with a formula?