It can certainly be done. Identifying the fifteen dogs as A to O, here is one such arrangement:
|
Monday |
Tuesday |
Wednesday |
Thursday |
Friday |
Saturday |
Sunday |
|
A-F-K |
A-B-E |
B-C-F |
E-F-I |
C-E-K |
E-G-M |
K-M-D |
|
B-G-L |
C-D-G |
D-E-H |
G-H-K |
D-F-L |
F-H-N |
L-N-E |
|
C-H-M |
H-I-L |
I-J-M |
L-M-A |
G-I-O |
I-K-B |
O-B-H |
|
D-I-N |
J-K-N |
K-L-O |
N-O-C |
H-J-A |
J-L-C |
A-C-I |
|
E-J-O |
M-O-F |
N-A-G |
B-D-J |
M-N-B |
O-A-D |
F-G-J |