Students search for the PDF because:
Real analysis is a gatekeeper course. If you copy a solution from a bootleg PDF for Problem 25 in Chapter 4 (Uniform Continuity), you are only cheating yourself. Analysis is learned by struggling . The "Aha!" moment when you finally prove that the image of a compact set is compact is the entire point of the class.
Before hunting for solutions, one must understand the enemy. Pugh’s Real Mathematical Analysis is not Rudin. Where Rudin is a fortress of definitions-theorem-proof, Pugh is a narrative. He includes historical context, witty asides, and—most famously—detailed drawings.
Instead of spending ten hours hunting for a mythical complete PDF, spend those ten hours wrestling with three hard problems, posting on StackExchange, and forming a study group. By the time you complete Pugh’s Chapter 8 (Metric Spaces), you will realize you no longer need a solutions manual—because you have become a mathematician capable of verifying your own proofs.
The difficulty of finding solutions mirrors the central lesson of real analysis: not every well-posed problem has an easily accessible, closed-form solution. Sometimes, you must construct the answer yourself from first principles.