Publishing elementary results As the title suggests, I am interested to know the chances of a middle-ranking journal's acceptance of a paper by an unknown author, detailing comparatively elementary results. By elementary, I mean results which are simply stated and simply proven: requiring knowledge only up to perhaps undergraduate year 3 or 4 courses. The results are new but do not have any obvious implications, nor are they usually considered as well-known interesting questions (not like open questions posed by previous authors). The "interestingness" of the results are mediocre at best. The methodology involved is new, but there is nothing to show that it is applicable in other related problems in the field, nor that it is significant in any way beyond the paper. Note that the field I am interested in is mathematics.

So, what are the chances of a journal accepting such a paper? My initial reaction is that perhaps this kind of papers would seem too trivial, given that often papers published in journals consider material from the PhD level or beyond. But then again, it is novel research with results interesting to some, so perhaps they are worth publishing.

(You can assume that the results and methodology given in the paper are truly novel and correct.)
From your description it sounds like the results have no implications, no relation to other problems, and is not significant in any way beyond that paper. In that case, chances are journals will not accept the paper. A paper needs to convince the editors &amp; reviewers that its results are actually interesting.
Check out Steven Gubkin's answer to another question:

Here is a brand new mathematical theory I have invented just now (in the last 30 seconds):
A Gobleflump is a set together with a ternary operation Star(a,b,c), and a binary operation Spade(a,b) satisfying Star(Spade(a,b),Spade(c,d),Spade(e,f)) = Spade(Star(a,b,c),Star(d,e,f)).
I could now devote my life to the study of Gobleflumps. I could publish papers about extremely regular gobleflumps, and the equivalence between hyperconvex gobleflumps and hypoconvex grendleflops. This might all be legitimate, correct mathematics.
No one will ever care about my lifes work, or probably even read it, unless it makes some connection to existing mathematical theory, illuminates why something disconnected from the theory works the way it does, or solves some existing problem.

... and if no one will ever care about the results, most reputable journals will not publish them, either.