As algorithms are given responsibility to make decisions that impact our lives, there is increasing awareness of the need to ensure the fairness of these decisions. One of the first challenges then is to decide what fairness means in a particular context. We consider here fairness in deciding how to match organs donated by deceased donors to patients. Due to the increasing age of patients on the waiting list, and of organs being donated, the current "first come, first served" mechanism used in Australia is under review to take account of age of patients and of organs. We consider how to revise the mechanism to take account of age fairly. We identify a number of different types of fairness, such as to patients, to regions and to blood types and consider how they can be achieved.