Hi Selmer, Just wondering if you received the papers. If not, please let me know and I'll fax them to you tomorrow. Here's a reference for Collatz's problem: Gardner 1983] Martin Gardner, Wheels, Life, and Other Mathematical Amusements. W. H. Freeman. New York: 1983. Page 196. If you'd like more references, check out http://www.wwa.com/math/puzzles/unsolvedMathProblems/references.html That document contains more than a dozen references to the problem. Yrs, Kostas