Unlicensed Repair: When Large Language Models Turn Impossible Quantities into Plausible Answers

When solving word problems, large language models can explicitly identify an intermediate value they compute as impossible, such as a negative count of pallets, yet still produce plausible-looking answers. We study unlicensed repair: responding to a conflict between a computed value and an implicit commonsense constraint on its quantity with a modification the problem does not license. We construct an English–Chinese corpus in which every violated constraint is implicit, spanning multiple quantity types and distinguishing problems that license a repair from those admitting no consistent answer. Each violating problem has two controls: one changes an input so the value becomes legal, and the other keeps the value and changes what it represents. We evaluate $17$ models on $129,600$ model–prompt pairs with an LLM judge, checked against three independent annotators and a rule-based scorer. Pooled accuracy is lower on violating problems than on either control. Across all $17$ models, the gap to the first control is larger when no repair is licensed: $63.2$ against $11.8$ percentage points pooled. Most incorrect responses explicitly acknowledge the conflict. When no repair is licensed, almost all of those that acknowledge it go on to perform exactly this repair: they alter premises or introduce unsupported assumptions, then commit to a plausible alternative. No lever we tested closes the gap: not more parameters, a newer model generation, a prompt to check, or reasoning. A plausible final answer can therefore conceal an unresolved contradiction that the model has explicitly identified.