Final answer:
In a hospital's master patient index, when individuals share the same surname and first name, the patient number is the most reliable and unique identifier to arrange the cards, as it is a distinctive attribute assigned to every patient.
Step-by-step explanation:
If more than one person with the same surname and first name has been admitted to hospital, the master patient index cards are usually arranged by an identifying factor that is unique to each patient. Among the options provided (date of birth, date of discharge, middle name, patient number), the most reliable and unique identifier would be the patient number. The patient number is a unique identifier assigned to an individual when they first become a patient at a hospital. It helps to distinguish between individuals who may share the same first and last names and, unlike the date of birth or middle name, it cannot be shared by two patients. Moreover, the date of discharge would not be known upon admission and middle names may not be unique enough. Therefore, the correct answer is d. patient number.