Thank you for making your solutions available to the forum members, for a short period.
All of the solutions are very concise. A number of the solutions are very clever. I especially like the application of Euler's formula in #28 (though it requires you to observe that all trees are planar graphs).
However, some of the other solutions appear to have typo's, and others may have material errors in calculation. For example, the integral substitution in #31, the algebra in #37, or the application of the chain rule in #63 do not look correct. Reading through the solutions, I compiled a list critical analysis-- I will mail these to your email address above. (If any forum members are using these solutions and interested in this list, I am willing to share it with them as well).
Also, if you'd like to compare and contrast with some other solutions, I've posted a set here (http://www.gigauploader.com/file/0770203183169331
). Here's a forum post: (http://www.mathematicsgre.com/viewtopic.php?f=1&t=1378