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?