Meta-reasoning refers to processes by which people monitor problem-solving activities and regulate effort investment. Solving is hypothesized to begin with an initial Judgment of Solvability (iJOS)--the solver's first impression as to whether the problem is solvable--which guides solving attempts. Meta-reasoning research has largely neglected non-verbal problems. In this study we used Raven's matrices to examine iJOS in non-verbal problems and its predictive value for effort investment, final Judgment of Solvability (fJOS), and confidence in the final answer. We generated unsolvable matrix versions by switching locations of elements in original Raven's matrices, thereby breaking the rules while keeping the original components. Participants provided quick (4 s) iJOSs for all matrices and then attempted to solve them without a time limit. In two experiments, iJOS predicted solving time, fJOS, and confidence. Moreover, although difficulty of the original matrices was dissociated from solvability, iJOS was misled by original matrix difficulty. Interestingly, when the unsolvable matrices were relatively similar to the originals (Experiment 2), iJOSs were reliable, discriminating between solvable and unsolvable matrices. When the unsolvable matrices involved greater disruption of the rules (Experiment 1), iJOS was not consistently predictive of solvability. This study addresses a gap in meta-reasoning research by highlighting the predictive value of iJOS for the solving processes that follow. The study also provides many future directions for meta-reasoning research in general, and regarding non-verbal problems, in particular.