Start with any whole number. Call it A. Find the next integer B in the following way: If A is odd, then B = 3A + 1; if A is even, then B = A/2. Continue generating numbers one after the other in this way. Examples: 1--> 4--> 2-->1 and 3--> 10--> 5--> 16--> 8--> 4--> 2--> 1. Do you always get 1 regardless of which whole number you start with? Extensions of the problem and a discussion of the underlying mathematical ideas are included. This mathematically rich problem was originally developed for the Project Discovery Mathematics by Inquiry institutes for middle grades teachers taught in 1992 - 1994 at Ohio State University. Project Discovery was co-funded by the Ohio Board of Regents and the Statewide Systemic Initiative (SSI) program of the National Science Foundation. (author/sw)