In order to score for the fragile X syndrome, blood samples are prepared with absorption stain labeling by in situ hybridisation of the X chromosome centromeres. Metaphases are located, digitised at high resolution, and segmented fully automatically. A three stage adaptive classification scheme for labeled X chromosomes is then applied. This consists of a simple box classifier to identify plausible X and false positive X chromosomes, followed by a quadratic discriminant classifier that is re-trained for each sample. The modal number of X chromosomes is then determined for each sample and used to refine the classification. A simple fragile site detector is applied to the distal portion of the detected X chromosome long arms. From the results we estimate computer and operator time requirements for a screening system in which the operator reviews only the apparently fragile X chromosomes detected by the computer.