The +1 makes the range inclusive rather than exclusive. This matches the summary, which is inclusive of floor(500/k). Ceil wouldn't correctly handle the case where the number of rooms equals a perfect square. That is,
[k**2 for k in range(1, ceil(484**0.5))]
Incorrect. Here's the summary reproduced (in case susam edits again):
>>> There are 500 doors numbered 1, 2, ..., 500. All doors are closed initially. In iteration k, we toggle the states of doors k, 2k, ..., floor(500/k) * k where k runs from 1 to 500
Note the "floor(500/k)" statement. That matched the original code fragment (and what is still sitting in a terminal on my laptop):
but not the new one which includes a +1. int(…) is floor. int(…)+1 isn't, and it's wrong: It works for 500, but not for other values. math.ceil would have been more correct, but it might've been more obvious that it doesn't match the "summary".> (if it really existed).
Let me make sure I understand what you mean here: You actually think it more likely that my two implementations, written in a comment [1] with a lower timestamp than [2], and the perl6 implementation on the linked article all include 484 as part of the valid result, and yet my comment [2] that calls on this value specifically, was somehow meant to indicate that 484 is not part of the valid result?
Ha.
[1]: https://news.ycombinator.com/item?id=22288534
[2]: https://news.ycombinator.com/item?id=22288554