BMAD Posted June 27, 2013 Report Share Posted June 27, 2013 Fifteen college teachers (A,B,...,O) must serve on a total of twenty committees (1-20), such that: i) Each teacher is on exactly four committees, ii) Each committee has three teachers on it, iii) No two committees have more than one teacher in common. List (or accurately describe) such a committee structure, or else prove it can't exist. Quote Link to comment Share on other sites More sharing options...
0 superprismatic Posted June 28, 2013 Report Share Posted June 28, 2013 A 1 in row i and column j of this matrix indicates that teacher i is assigned to committee j.11110000000000000000 00001111000000000000 00000000111100000000 00000000000011110000 00000000000000001111 10001000100010000000 01000100010000000100 00100010000000100010 00010000000100010001 00000001001001001000 10000100001000010000 00001000010000100001 00010000100001000010 00100001000010000100 01000010000100001000 Quote Link to comment Share on other sites More sharing options...
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