You can also solve this in O(logn) using a physical binary search:

1) Move half the boxes to another room.

2) Listen for a beep and determine which room the beep comes from.

3) Take the boxes in that room and split them in half again.

4) Repeat until one box is left.

It's O(logn) but you haven't accounted for how heavy each item in the array of n is.

Or you could use a very heavy blanked to just cover some boxes to supress the sound enough to simulate moving boxes.

Yes, but that's also O(log n) physical effort. This one's O(1) sitting on your butt.

(Out of curiosity: I think "physical binary search" is more properly O(n^{1/3} log(n)), or maybe O(n^{1/2} log(n)). Since physical objects have sizes, and moving things (or moving between things) takes time proportional to distance).

That requires you to stand in the room and listen for which side. So it’s nlogn times a very long time constant

> Move half the boxes to another room.

Alternatively, no.