Should I acknowledge the source of a problem in a math assignment?
I often assign "challenge" problems for my Calculus class that are drawn from Apostol (similar in difficulty, etc., to Spivak).  For the reasons you describe above, I prefer not to reveal the source of the problem.  My solution has been to label the problem as a challenge problem, and say that it comes from a classic (read: hard) textbook on Calculus when I assign the problem. However, I don't specify which textbook that is on the assignment.  After the problem set is due, I give the students the full reference.  Of course, my hope is that some of them found the problem interesting and will go look up more problems to challenge themselves.

I think this compromise works since you are not taking credit for creation of the problem, and do give acknowledgement.  Of course, with all of these students can find the answers through diligent searching, but I think raising the barrier even a little is a good idea.