OBJECTIVE The study addressed the question of whether unsolvable as opposed to solvable cognitive problems activate discrete neuronal systems in the human brain. METHODS Twelve healthy humans tried to solve unsolvable anagrams. Solvable anagrams and a resting baseline after each anagram task served as control conditions in a within-subject design. Activation was measured with the equilibrium infusion method by using 15O-labeled water and positron emission tomography, with absolute quantitation of anatomically defined regional cerebral blood flow (CBF). RESULTS Compared to rest, both anagram tasks increased activity in frontal and temporal regions. The soluble task condition increased hippocampal activation and decreased mammillary bodies activity, while unsolvable anagrams were associated with increased CBF to the mamillary bodies and amygdala and decreased hippocampal activity. CONCLUSIONS A limbic network integrating negative emotion and cognition seems reflected in reciprocal diencephalic and limbic activation with solvable and unsolvable anagrams. Since unsolvable anagrams have been used to induce learned helplessness in humans, this finding may provide an initial step toward clarifying its neural substrate.