Arrgh. Typo fixed. It seems that I have a 100% success rate in catching my typos within 15 seconds of clicking the “Publish” button. I had fixed the typo after I published this post, but before I received your email. If only I had been a bit better at editing, I could have saved you the trouble of catching my error!

Intuitive? Hmm. Not sure. Seems that opening/closing lockers and turning lights on/off in such a pattern seems counter to anything I think kids would do on their own. I prefer problems that are more real… but I tolerate contrivance if it leads to a good result.

]]>4, 8, 9, 12, 16, 18, 20, 24, 25, 27, 28

@1: Yes, as can easily be seen by looking at Möbius (Dirichlet) inversion modulo 2 (or just by induction).

]]>A generalization: Is there some set of students that corresponds to every possible final state of the lockers?

And a comment: I heard a version of this problem where it was light bulbs instead. Pulling the light bulb string seems much more intuitive that switching the state of the locker.

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