There is an (immobile) object in a node except for a specified node, with a priori probabilities. A seeker starts at the specified node and examines each node until he finds an object, traveling along edges. Associated with an examination of a node is the examination cost, and associated with a movement from a node to a node is a traveling cost. A strategy for the seeker is an ordering of nodes in which the seeker examines each node. The purpose of the seeker is to find a strategy which

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... s the expected cost. Necessary conditions for a strategy to be optimal are presented. Special cases are solved.