IrMO 1991 Problem 4

Eight politicians stranded on a desert island on January 1st, 1991, decided to establish a parliament. They decided on the following rules of attendance:

(a) There should always be at least one person present on each day.

(b) On no two days should the same subset attend.

(c) The members present on day $N$ should include for each $K<N$ , $(K\ge 1)$ at least one member who was present on day $K$ .

For how many days can the parliament sit before one of the rules is broken?