# “This problem has no solution”: when closing one of two doors results in failure to access any.

- Hippolyte Gros,
*University Paris Descartes, Sorbonne Paris Cité, Paris, 75006, France*
- Emmanuel Sander,
*Paragraphe Lab, EA 349, University Paris 8, Department of Psychology, 2 Rue de la Liberté, 93526 Saint-Denis Cedex 02, France.*
- Jean-Pierre Thibaut,
*LEAD-CNRS, UMR 5022, UB, Univ. Bourgogne Franche-Comté, Pôle AAFE – Esplanade Erasme, 21065 Dijon. France.*

## Abstract

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.

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