A computer science department has eightcommittees,and professors{A,B,C,D,E,F,G,H

Question

A computer science department has eightcommittees,and professors{A,B,C,D,E,F,G,H,I,J} are assigned to these committees as follows.

Computing {A,B,C,D}

Library {A,E,F,G}

Recruitment {G,H,I,J}

Tenure & Promo {H,B,F}

Advising {D,E}

Curriculum {C,A}

Fund Raising  {I,G}

Outreach {J,C}

If each committee is scheduled to meet for a hour, waht is the smallest number of hours required to schedule all eight committee meetings so that every professor is able to meet with all the committees to which he or she is assigned?

Explanation / Answer

Number of committes that each professor is a member of:
A- 3; B- 2; C-3; D-2; E-2; F-2; G-3; H-2; I-2; J-2

Thus from this we can say that at least 3 hours of time is required;
In each hour, the members with 3 memberships have to have their meeting;
Hour 1: Computing, Fund Raising
Hour 2: Library, Outreach
Hour 3: Curriculum, Recruitment, Advising
Hour 4: Tenure and Promo

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