A Committee Structure
We will consider a structure for creating committees that will be efficient
and effective in designing programmatic changes for all members of an organization.
Conditions for a Committee Structure
-
Each committee will have exactly three members.
-
Any two committees will have exactly one member in
common.
-
Any two members determine a unique committee.
-
There are at least two committees.
Here are two examples:
Notice that each structure has 7 committees and 7 members!
| C |
E |
G |
|
|
G |
B |
C |
| B |
D |
G |
|
|
G |
D |
F |
| A |
F |
G |
|
|
G |
A |
E |
| A |
D |
E |
|
|
C |
E |
D |
| B |
F |
E |
|
|
D |
A |
B |
| A |
B |
C |
|
|
C |
A |
F |
| D |
F |
C |
|
|
B |
F |
E |
Interesting....these were the same arrangements used for the chord stuctures.
But the question we have now is:
Are there any of these committee
stuctures that have more or less than 7 committees made from 7 members?
That is, is there some special
relation between these committee structures and the number 7?