We propose a model for the recognition of unconstrained digits that may be touched with neighbor ones or damaged by noises such as lines. The recognition of such digits seems to be rather paradoxical because it requires the segmentation of them into understandable units, but proper segmentation needs a priori knowledge of the units and this implies recognition capability. To break up the loop of their interdependencies, we combine two schemes, hypothesis testing and data reconstruction, motivated by the human information system. Hypothesis is set up on the basis of the information obtained from the results of the basic segmentation, and reconstruction of the information is carried out with the knowledge of a guessed digit and then testing for its validity is performed. Since our model tries to construct a guessed digit from input image it can be successful in a variety of situations such as that a digit contains strokes that do not belong to to it, that neighbor digits are touched with each other, and that there are some occluding things like lines. The recognition results of this model for 100 handwritten numeral strings belonging to NIST database and for some artificial digits damaged by line demonstrate the potential its capacity.