the relationship isn't many-to-many, because each problem can be related to only one serialnumber
as you suggested, it requires a third "relationship" table
furthermore, with the current structure, if you wanted to list some problems together with the PC or equipment they dealt with, you would have to conditionally join the problem table to two tables
finally, the serialnumber in the problem table cannot be declared as a database FK (even though you might use it that way -- for example, FKs are used in mysql all the time, even though mysql doesn't support FKs)
your reason stated for "wasting space" is not that big a deal, since you would declare those fileds null and thus they would take up no space (just the null bit)
rudy
http://r937.com/