There is a lot of good stuff contained in the Problems section of the American Mathematical Monthly. One difficulty with extracting that information, however, is that if I see an old Monthly problem, it is not always so easy to locate the solution. Sometimes the solution does not appear until many years later, and in some cases the solution has never appeared at all. For those at an academic institution with access to JSTOR, sometimes an electronic search will turn up the solution, but if the search comes up empty, I am left wondering whether the solution was really never published or whether I just did something wrong with my search. Furthermore, even with JSTOR access, there is no easy way to list (for example) all unsolved Monthly problems.
Does anybody have, or know of, an index of all the Monthly problems and solutions that would address this issue? Failing that, is there any interest in creating such a publicly available resource? If the work is divvied up among a few dozen volunteers it shouldn't take that much work. As I envisage it, the index would (at least initially) not contain the mathematical content of the problems but would just give the bibliographic information for the problem and the solution (if any), and indicate which parts (if any) remain unsolved.
Best Answer
This is somewhat redundant with Igor Pak's P.S., but I found an index for the 1918-1950 range in The Otto Dunkel memorial problem book, starting on page 80 of this pdf.
I found more: Stanley Rabinowitz and others had the same idea a couple of decades ago, and they started compiling indices, not just for the Monthly. Here are Google Books and official links for the two volumes I found:
1975-1979 (published 1999) Website
1980-1984 (published 1992) Website, Errata
Googling "Stanley Rabinowitz 1985-1989" led me to this:
I don't know if the 1985-1989 index was ever finished, but presumably there's at least a partial draft out there somewhere. The website http://www.mathpropress.com/ of Rabinowitz's company includes contact information. They say they're looking for authors to publish, among other things, "indexes to mathematical problems or results", but the page apparently hasn't been updated since 2006.