I am struggling to see the complexity of the following combinatorial search problem. Could anyone help me?
Consider a set $I$ of $n$ items known to contain $d$ defectives or less. Assume $d < n/2$. One chooses a set $S$ with exactly $n-d$ items in each test. If the set $S$ has no defectives, then the test function $f(S)=1$, otherwise $f(S)=0$. How many tests would one need to know which items are defectives?