reply on: [Daily puzzle] Locker problem \ stacker news ~science

264 sats \ 8 replies \ @Scroogey 2 Nov \ on: [Daily puzzle] Locker problem science

Lockers 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 are open at the end, all others are closed.

I.e. the square numbers!

I was about to confidently type 1, but I neglected the description about how people needed to open the lockers when they were closed during their turn. Darn it!

1 sat \ 5 replies \ @Undisciplined 2 Nov

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.

386 sats \ 2 replies \ @Scroogey 2 Nov

I think the answer is in 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.

1 sat \ 1 reply \ @Undisciplined 2 Nov

That makes a ton of sense

12 sats \ 0 replies \ @south_korea_ln OP 2 Nov

Indeed! 👍

10 sats \ 1 reply \ @south_korea_ln OP 2 Nov

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

1 sat \ 0 replies \ @Undisciplined 2 Nov

Fair enough

1 sat \ 0 replies \ @south_korea_ln OP 2 Nov

TIL: a one liner to toggle a variable between values of 0 and 1. Elegant.

a[j] = 1 - a[j]