Patients affected by Alzheimer’s disease (DAT) showed considerable difficulties assessing the numerosity of complex dot patterns (up to 30 dots). Patients’ and controls’ performance was found to be modulated by the spatial array of dot patters. Dots presented in curved lines were easier to count than dots in circle arrays or in random arrays. Highly significant between group differences were found in counting dots in circle arrays, but not in counting curved lines. Patients and controls differed in the choice of counting strategies. While controls efficiently adapted their counting strategies to the respective dot patterns, DAT patients were not able to adapt counting strategies to the requirements of the spatial arrays. Analysis of error types further evidenced the particular difficulties of patients. Several recounts in counting circle arrays reflected difficulties to stop counting, while omissions in random patterns suggested deficits in monitoring already counted items. Results of this study suggest that deficits in executive functions prevented patients from selecting and adapting counting strategies in order to keep track of already counted items, to enhance accuracy and to reduce demands on cognitive resources.