This is the most famous question on Stackoverflow and should have a protected status.
Can we make this impossible to close?
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It's fun to have a limited number of "fun" questions. The problem is that they set a bad example. They serve as an excuse for more "fun" questions.
I mostly think these should be subject to the will of the community. My "will" is likely to be to close them. However, a good fun question is likely to be reopened. In fact, over its life, I think it's likely to go through several close/reopen cycles, and maybe even close/delete/undelete/reopen. That makes it a really bad example.
I propose that we create a special site for those, maybe fun.stackoverflow.com. What's really special about this site would be that it does not accept new questions. Instead, a moderator may manually migrate a surviving "fun" question (after six months, say), from SO to FSO. We'd be able to add new answers to the question, but it would be off of SO, and the front page of SO, and would stop being a bad example.