My pick would be Volume 1 of Richard Courant and Fritz John's Introduction to Calculus and Analysis. For discussions of how Courant/John compares with Spivak, Apostol, and other books, see the math StackExchange question Difficulty level of Courant's book.
Volume 1 of Courant/John does not have any solutions to the exercises, but complete solutions to all the problems were separately published by A. A. Blank:
Albert Abraham Blank, Problems in Calculus and Analysis, John Wiley and Sons, 1966, x + 264 pages.
You might also want to look at the list of honors calculus books posted in the following math StackExchange question:
Joseph Kitchen's Calculus (reference)
(ADDED NEXT DAY) Regarding Joseph Malkevitch's answer, yesterday I was thinking of mentioning some books from roughly the 1880s to 1890s, when textbooks in algebra through calculus were, on average, pitched at the highest level, but I didn't get around to it. Throughout the 1800s there was a gradual overall trend towards more difficult texts until the end of the 1800s, at which time there were several "downward adjustments" (I'm mostly thinking of the U.S. and England) due to various reforms and the increasing percentages of students going to college. (This is discussed in Châteauneuf  for those wishing a reference.)
Off-hand, I can think of three authors from this time who wrote calculus treatises at a fairly high level (in the algebraic-manipulative-mechanical sense, not in the modern rigorous sense), and with the beauty of the internet now-a-days it only takes me a few minutes to track down freely available digital copies of their books. See  through  below. I think you'll find plenty of "extremely challenging exercises" in these books, and many will be on topics you are probably not familar with. The books by Edwards are probably the most extreme in this respect, and over the years I've read book reviews in old journals that pretty much say this (while also being very critical of Edwards' lack of rigor, especially in reviews written after the mid 1890s).
 Amy Olive Châteauneuf, Changes in the Content of Elementary Algebra Since the Beginning of the High School Movement as Revealed by the Textbooks of the Period, Ph.D. Dissertation (under John Harrison Minnick), University of Pennsylvania, 1929, x + 191 pages.
Also published by Westbrook Publishing Company in 1929, and reviewed by Lao Genevra Simons in Mathematics Teacher 24 #1 (January 1931), 58-59.
 Joseph Edwards, An Elementary Treatise on the Differential Calculus
 Joseph Edwards, A Treatise on the Integral Calculus, Volume 1
 Joseph Edwards, A Treatise on the Integral Calculus, Volume 2
 Isaac Todhunter, A Treatise on the Differential Calculus
 Isaac Todhunter, A Treatise on the Integral Calculus and Its Applications
 Benjamin Williamson, An Elementary Treatise on the Differential Calculus
 Benjamin Williamson, An Elementary Treatise on the Integral Calculus
Incidentally, solutions manuals to older texts (in English) were often called Keys, and I'm sure some of the texts above have keys (typically prepared by someone other than the text's author), which I'll leave you to search for if you're interested. I did happen to come upon the following Key while looking up the books above, so I'll include it:
Hunter, Key to Todhunter's differential calculus