Lets say you are given $n$ programs and you want to determine EXACTLY which ones halt. If you can ask the HALTING PROBLEM $n$ questions then you could certainly deterimine this. If you can ask the HALTING PROBLEM only $n-1$ questions then could you do this? More generally we ask the following: Let $A$ be a set and $n$ be a number. How hard, in terms of queries to $A$, are the following problems. 1) Given $n$ numbers, exactly which ones are in $A$? 2) Given $n$ number, how many are in $A$ ? 3) Given $n$ number, is the number that are in $A$ even? 4) Are there functions that can be computed with $n$ queries to $A$ that cannot be computed with $n-1$ queries to $A$. 5) Are there sets that can be decided with $n$ queries to $A$ that cannot be computed with $n-1$ queries to $A$.