Lynn Arthur Steen (2006). Asking the right questions. In Lynn Arthur Steen (Ed.) (2006). Supporting Assessment in Undergraduate Mathematics. The Mathematical Association of America. The chapter itself as pdf. The whole book is online as pdf
p. 3: "More than most disciplines, mathematics is defined by its problems and examinations, many with histories that are decades or even centuries old. National and international mathematical Olympiads, the William Lowell Putnam undergraduate exam, the Cambridge University mathematics Tripos, not to mention popular problems sections in most mathematics education periodicals attest to the importance of problems in defining the subject and identifying its star pupils. (...) for virtually everyone associated with mathematics education, assessing mathematics means asking students to solve problems."
Steen mentions Archimedes' 'cattle problem' in p. 3 box. It is a well known problem, see for example Weisstein html
p. 4:"Mathematician and assessment expert Ken Houston of the University of Ulster notes that these types of mathematics tests are a “rite of passage” for students around the world, a rite, he adds, that is “never to be performed again” once students leave university. Unfortunately, Houston writes, “learning mathematics for the principal purpose of passing examinations often leads to surface learning, to memory learning alone, to learning that can only see small parts and not the whole of a subject, to learning wherein many of the skills and much of the knowledge required to be a working mathematician are overlooked” (Houston, 2001). "
Stevens presents an old Indian problem in the box on p. 5.
Houston, Ken. (2001). “Assessing Undergraduate Mathematics Students.” In The Teaching and Learning of Mathematics at University Level: An ICMI Study. Derek Holton (Ed.). Dordrecht: Kluwer Academic, p. 407–422. html
Weisstein, Eric W. "Archimedes' Cattle Problem." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/ArchimedesCattleProblem.html
Shen Kangshen, John Crossley and Anthony Lun (Trlts, Eds) (1999). The nine chapters on the mathematical art. Companion and commentary. Oxford University Press site & Being: Science Press, price: astronomical.