I think the answer is in [Why do perfect squares have a odd amount of factors](https://math.stackexchange.com/questions/3358685/why-do-perfect-squares-have-a-odd-amount-of-factors)

The squares are exactly those numbers with an odd amount of factors. Because the amount is odd, they are now open.

Scroogey

There is an intuitive argument. But I'll give it some more time before divulging it.

south_korea_ln

I get that the primes will all be closed, because only the corresponding prime'th student will toggle that locker, but I don't see a clever argument for just the squares being left.

science

[Daily puzzle] Locker problem

I'd love some intuition for this result.

I get that the primes will all be closed, because only the corresponding prime'th student will toggle that locker, but I don't see a clever argument for just the squares being left.