# Why is this question considered undergraduate?

The question https://mathoverflow.net/questions/173132/number-of-combinations-of-ordered-sequences-of-n-integers is closed because it is considered "undergraduate"... could someone explain me how in the world an undergraduate student will solve it? IMO, the solution does not involve simple Combinations and Permutations.

• As I said in the comments, it has an easy elementary solution that you're missing. And in fact sometime back in the 20th century I remember being asked to solve an isomorphic problem on the homework in an undergraduate combinatorics class. – Andy Putman Jul 2 '14 at 20:54
• The meta question is fine, I see no need to downvote the meta question (even if the comments on main are not so great). – user9072 Jul 2 '14 at 21:03
• @quid This question was probably downvoted because of the tone. The Masked Avenger explained very well how to solve the problem in a comment at MO, and yet the OP seems to reject the explanation. – Todd Trimble Jul 3 '14 at 13:38
• you can ask anything for a student, even if he is undergraduate. Whether he will manage to solve it in available time is another matter. – user38397 Jul 3 '14 at 14:47
• @ToddTrimble thanks for the comment. But please note that the meta-post predates any comment (at least non-deleted ones) of The Masked Avenger and not much time eleapsed between the posting and the first dv (as docuemented by the time of my comment); I am thus not convinced your explanation is a good one. – user9072 Jul 4 '14 at 13:32
• @quid You can ignore the timeline and any mention of mine of the Masked Avenger's comments (i.e., take that mention as mere addendum and not 'explanation'), and the tone is still bad. – Todd Trimble Jul 4 '14 at 13:40
• @ToddTrimble even admitting this, what is gained by downvoting it? (Note that I said I see no need, so if you want to disagree with me you should explain the need.) – user9072 Jul 4 '14 at 13:56
• @quid I don't disagree with you. Nothing is particularly gained by an unexplained downvote, but for the benefit of the OP, it might be helpful to know a likely reason for the downvotes. – Todd Trimble Jul 4 '14 at 14:11
• @ToddTrimble glad this is clarified. I am pretty sure that some will/would have read your first comment as justifying unexplained downvotes on such questions, whence my reaction. – user9072 Jul 4 '14 at 15:53

It does have an elementary solution, as I indicated in a comment that was discouraged by Andy Putman.

I will not tell you the worked out answer, and opinions here vary as to what contributes an answer. In any case , it is material that is covered in elememtary combinatorics texts, and is considered by me and many others as undergraduate level or earlier.

I would appreciate a remark from you, the OP on what is the best way to redirect you to math.SE, which is more appropriate. Did I say too much? Did I take too much of the process of learning away from you? Is Andy Putman right, and I should just say "go to math.SE"? I am interested in a candid response from you.

• I don't know if you can comment on this answer. You should be able to post a response as another answer or question edit. Not optimal, I know. – The Masked Avenger Jul 2 '14 at 21:22
• Of course OP can comment here. From the help center "Please note that you can always comment on your own posts, and any part of your questions." (my emph) – user9072 Jul 2 '14 at 21:28
• The OP asked the question on math.se and has already accepted an answer, so I doubt we'll hear from them again : math.stackexchange.com/questions/854745 – Andy Putman Jul 2 '14 at 21:46
• @Andy, if you're right, mission accomplished. I still have the opinion a different approach was needed here. Moving on to more productive pursuits... – The Masked Avenger Jul 2 '14 at 21:52
• @AndyPutman I fully agree that the question is off-topic, but I also think that OP honestly thought the question is on-topic here. (Why would they ask it here, and not on math.SE where they had asked various questions before? Some of them seeming harder than that one.) I thus believe (with the benefit of hind sight) that a more clear/detailed indication why the question is off-topic would have been better. Perhaps also worth noting that the question got a vote to reopen. – user9072 Jul 2 '14 at 22:02
• @quid : I suspect that the vote to reopen came from the OP (you can vote to close and open your own questions). As far as how to convince the OP that it was elementary, I'm not really sure how to do so without telling them how to solve it, which I think is inappropriate and likely to lead to more bad questions. Any suggestions you have would be appreciated. – Andy Putman Jul 2 '14 at 22:21
• @AndyPutman The reopen vote cannot have been OP. Voting ones own question also needs some points (namely 250). I disagree that it is likely that giving a quick but clear pointer in the comments will contribute in any relevant way to more bad questions. Or, at least, the contribution would be so small that I consider it as relatively less bad than the comment and meta noise we had. (But it is hard to quantify this and ones priorities can reasonably be different here, so I guess in the end all we can do is to agree to disagree.) – user9072 Jul 2 '14 at 22:53
• @quid : Interesting, I did not know that. I'm a little surprised that a high-rep user would have voted to reopen, but who knows? Anyway, I suspect that both of us understand each other's point of view, and that is probably the best that can be accomplished in this situation. – Andy Putman Jul 2 '14 at 22:55
• Indeed, I asked the same question on Math.SE. It would be more nice and more efficient if the suggestion to redirect it to Math.SE came at first place. It simply is not efficient to close the question and write "it has elementary solution". It might be elementary, but I was looking for a solution anyways (or at least an advice on my path). I am running a PhD on engineering, thus I have no knowledge on combinatorics. For someone who wants to solve it starting from simple high school knowledge, it is not elementary nor trivial! – user38397 Jul 3 '14 at 14:38
• @user38397, thank you for your comment. I will try suggesting math.SE first next time. – The Masked Avenger Jul 3 '14 at 15:08
• @user38397 For someone who wants to solve it starting from simple high school knowledge, it is not elementary nor trivial! High school knowledge is a huge overkill for realizing that the answer is $1^{N-1}+2^{N-1}+\dots+K^{N-1}$ and the university education is barely enough to state what it means that it is not an elementary formula. On the other hand, you once more raised the question that I'm raising every time I can: Won't it be more useful for every conceivable objective (barring giving Stewart more easy income) to teach basic discrete math instead of some parts of cookbook calculus? – fedja Jul 4 '14 at 16:04
• @fedja, I think you solved a different problem. I get different numbers for K=2. – The Masked Avenger Jul 4 '14 at 17:57
• @fedja You are interpreting "bigger than or equal to the last one" differently from the Masked Avenger. You think it means $a_i \geq a_N$ for all $i$, Masked Avenger thinks it means $a_i \geq a_{i-1}$. Your count is $1+2^{N-1} + \cdots + K^{N-1}$; Masked Avenger's is a binomial coefficient. – David E Speyer Jul 7 '14 at 15:19
• @David, thanks for that bit of detective work. It lends support to the notion that fedja is not trolling, which was my hope. – The Masked Avenger Jul 7 '14 at 17:01
• @David Speyer Erm... True enough. Unfortunately, the example OP gave (N=2) doesn't allow to distinguish between the two and "the last in the list" is as common as "the last in the queue". As to the general question of trolling, I guess I may be on the borderline occasionally, but, at least, I try not to post when I have nothing to say, so if something I post looks strange, a failed communication is more probable than a malicious intent. Alas, for the last month I had no time to really think of MO questions, so I was posting more when "overwhelmed emotionally" than when "having a bright idea". – fedja Jul 8 '14 at 10:18

There are many questions, useful for research, that can be answered by bright undergraduates. If it does not look standard, why not put it into MO? The problem with the larger Math StackOverflow, it is dominated by 1-minute questions and answers.

• This point of view might have some merit to it, however in the current case a main reproach (as far as there is any) is that it is a perfectly standard "1-minute" question, that is if one has the right knowledge (if not one could well get stumped, it is not obvious either). This is exemplefied by the question in fact having been answered quickly on Mathematics Stack Exchange once asked there. – user9072 Jul 8 '14 at 20:30