Initial Judgment of Solvability (iJOS) is a metacognitive judgment that reflects solvers’ first impression as to whether a problem is solvable. We hypothesized that iJOS is inferred by combining prior expectations about the entire task with heuristic cues derived from each problem’s elements. In two experiments participants first provided quick iJOSs for all problems, then attempted to solve them. We manipulated expectations by changing the proportion of solvable problems conveyed to participants, 33%, 50%, or 66%, while the true proportion was (...) the 50% for all. In Experiment 1 we used the non-verbal Raven’s matrices and examined nameability as the element-based heuristic cue. Unsolvable matrices were generated by switching locations of elements in original Raven’s matrices. In Experiment 2 we used the verbal Compound Remote Associate (CRA) problems and examined word’s frequency in the language as the element-based heuristic cue. Unsolvable CRAs were random word triads from the same word pool. The results were consistent in suggesting that quick iJOS integrates prior expectations and experience-based heuristic cues. Notably, iJOS was predictive for the subsequent solving attempt only for Raven’s matrices. (shrink)