A doctor is scheduling one appointment each with five patients— J, K, L, M, and N. The five appointments will be consecutive and are numbered 1 through 5, from earliest to latest. The doctor must schedule at least four of the patients for appointments preferred by those patients and cannot schedule any patient for an appointment unacceptable to that patient. The following is a complete list of what the patients prefer and, if they do not receive their preferences, will accept:
J prefers an appointment earlier than appointment 3, but will accept any appointment.
K prefers appointment 2, but will accept any appointment except appointment 1.
L prefers appointment 1, but will accept appointment 5.
M prefers and will accept only an appointment later than appointment 3.
N prefers and will accept only appointment 3.