We investigated what happens when the spontaneous encoding of a problem is incongruent with its solving strategy. We created word problems from which two distinct semantic representations could be abstracted. Only one of these representations was consistent with the solving strategy. We tested whether participants could recode a semantically incongruent representation in order to access another, less salient, solving strategy. In experiment 1, participants had to solve arithmetic problems and to indicate which problems were unsolvable. In experiment 2, participants received solved problems and had to decide whether the solution was appropriate or not. In both experiments, participants had more difficulties acknowledging that problems inducing an incongruent representation could be solved than they had for problems inducing a congruent representation. This was confirmed by response times. These results highlight how semantic aspects can lead even adults to fail or succeed in the solving of arithmetic problems requiring basic mathematical knowledge.