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We consider a variant of the planted clique problem where we are allowed unbounded computational time but can only investigate a small part of the graph by adaptive edge queries. We determine (up to logarithmic factors) the number of queries necessary both for detecting the presence of a planted clique and for finding the planted clique. Specifically, let $$G \sim G(n,1/2,k)$$ be a random graph on $$n$$ vertices with a planted clique of size $$k$$. We show that no algorithm that makes at most $q = o(n^2 / k^2 + n)$ adaptive queries to the adjacency matrix of $$G$$ is likely to find the planted clique. On the other hand, when $$k \geq (2+\epsilon) \log_2 n$$ there exists a simple algorithm (with unbounded computational power) that finds the planted clique with high probability by making $$q = O( (n^2 / k^2) \log^2 n + n \log n)$$ adaptive queries. For detection, the additive $$n$$ term is not necessary: the number of queries needed to detect the presence of a planted clique is $n^2 / k^2$ (up to logarithmic factors).