The following problem can be solved by generating and organizing relevant data and looking for patterns. The problem is challenging but does not require sophisticated mathematics.
Problem. In an effort to keep up with the expanded menu of competitors, Hal's Hamburger Haven now sells "chicken chunks" in boxes of 6, 9, and 20. Notice that some amounts of chunks cannot be purchased; for example, you cannot buy 8 or 14 chunks. Why? What is the greatest number of chunks that you cannot buy at Hal's?