@Peter I don't agree that it is "utterly ok". Anyone can say "I started with a proof by contradiction" for any mathematical question at all, so it shows absolutely no real effort. But I like that you gave only a hint in the comments, which ought to be the way instead of providing answers to a no-effort question.
@Peter Are you aware that there are a number of people who have similar obsessions on Math SE who (naturally) upvote one another's posts even if they make no sense? That post has been deleted anyway (before I saw it).
@Peter: there are many FGITWs here. Any routine question usually gets an answer within few minutes. Ask a non-routine question and you need to wait longer.
@XanderHenderson, @user21820: I couldn't do it in 90 secs. But maybe because I have become lazy. If this came in some time based exam I would have managed in 120 secs.
@XanderHenderson: also the tone of asker was rather defensive when replying to your royal road comment.
@ParamanandSingh Yeah. Obviously, I was supposed to know from context that they were looking for a royal road on behalf of their students, rather than for themselves. :\
I have not yet experienced to have run out of delete-votes, I only occasinally ran out of votes for comments :)
Not that it is IMPOSSIBLE to solve this in $90$ seconds , but this time period is nevertheless ridiculously short. Maybe, it is a casting for masters of mental calculating.
@Peter I don't think it's impossible. When I was a high-school student long long ago, I probably could do much more complicated problems than that in that kind of time, simply because I was regularly doing contest mathematics.
That said , it seems that being used to solve problems of the particular kind helps to being fast, since one knows then the tricks that are necessary for such a speed. If one did not do such exercises for a long time, one will take much longer, I guess.
@user21820 I can (and did), but I didn't want to remove the original target until I had decided what to do about the two questions. It took time to read the questions and make a decision.
@user21820: handled all D's. While checking the question in D11 a funny thing happened. The question is edited by some user named Bjorn and the username is displayed in very weird manner on my mobile device.
@XanderHenderson I wrote a couple of comments below this meta question. If my last comment seems to be over the top, let me know. @ParamanandSingh, @user21820, @MartinR, @Peter, also, if you have any input on how best to answer, I'd love to hear it.
Oops, @ParamanandSingh, You might already be in bed.
@amWhy I think you have found already the right answers. In fact, some cases of upvoting machinerie are suspicious. There is no satisfaying alternative explanation.
In fact. Since this cannot be prevented anyway, we should at least remove most of the $50$ posts with a score of $-8$ or less. Most of them should be worth being deleted if the score is so negative.
@amWhy If I had nothing better to do, my question regarding that graphing question would be: "Is this laziness for real?" Then again, I guess I have better things to do.
