Cryptography Problem, deals with secret sharing schemes.

When the College of Arts at Pedantic University wishes to have a business faculty meeting certain quorum rules are in place. There are four departments within the College; Literature, History, Languages and Philosophy and these contain 20, 17, 11 and 15 faculty respectively. To form a quorum there must be at least two-thirds of the members of each department present and all departments must be so represented. Modern technology has entered the fray and the meeting will be completely online and such that it cannot be determined if any faculty member is participating.

a.) How would the Dean set up a secret sharing scheme to implement this scenario?

b.) The rules have now been modified to be such that a quorum only requires three departments to participate (but the two-thirds rule within a department still applies). How would the Dean now set things up?