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 of politicians attend.
(c) The members present on day N should include for each K < N, (K ≥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?
[IrMO 1991 Paper1 Question 4][slightly edited]
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