A Course Schedule Structure
We will consider a structure for scheduling courses that will be efficient
and effective in designing a daily course schedule.
Conditions for a Schedule Structure
-
Each course will meet on exactly three days.
-
Any two classes will meet on the same day exactly once.
-
Any two days determine a unique course meeting on those
two days.
-
There are at least two courses.
Here are two examples:
Notice that each structure has 7 courses and they meet
on 7 days!
| 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 other stuctures.
But the question we have now is:
Are there any of these course
schedule stuctures that have more or less than 7 courses meeting on 7 days?
That is, is there some special
relation between these course schedule structures and the number 7?