From (4), the partial seating arrangement of men and women around the table was either (M represents man and W represents woman):
(CASE I)
+---+ +---+
| W | | W |
+---+ +---+ +---+ +---+ +---+ +---+
| M | | M | | M | | M |
+---+ +---+ +---+ +---+
+---+ +---+ +---+ +---+
| | o | | ====> | M | o | M |
+---+ +---+ +---+ +---+
+---+ +---+ +---+ +---+
| W | | W | | W | | W |
+---+ +---+ +---+ +---+ +---+ +---+
| | | W |
+---+ +---+
(CASE II)
+---+ +---+
| M | | M |
+---+ +---+ +---+ +---+ +---+ +---+
| M | | M | | M | | M |
+---+ +---+ +---+ +---+
+---+ +---+ +---+ +---+
| W | o | W | ====> | W | o | W |
+---+ +---+ +---+ +---+
+---+ +---+ +---+ +---+
| W | | W | | W | | W |
+---+ +---+ +---+ +---+ +---+ +---+
| | | M |
+---+ +---+Then, from (1) and (2), either (A represents Astor, B represents Blake, and C represents Crane):
(CASE I) (CASE II)
+---+ +---+
| W |(A) | M |
+---+ +---+ +---+ +---+ +---+ +---+
| M | | M |(B) | M |(B) | M |
+---+ +---+ +---+ +---+
+---+ +---+ +---+ +---+
| M | o | M | | W |(A) o | W |
+---+ +---+ +---+ +---+
+---+ +---+ +---+ +---+
| W |(C) | W | | W | | W |(C)
+---+ +---+ +---+ +---+ +---+ +---+
| W | | M |
+---+ +---+From (3), no man sat between a married couple; so, in Case I, Mrs. Blake sat opposite Mrs. Astor, But, then, no woman can sit between a married couple as required by (3); so, CASE I is eliminated.
Then, CASE II is the correct case. Then Mrs. Blake and Mrs. Davis were seated in one of the following ways (D represents Davis):
(CASE IIa) (CASE IIb)
+---+ +---+
| M | | M |
+---+ +---+ +---+ +---+ +---+ +---+
| M |(B) | M | | M |(B) | M |
+---+ +---+ +---+ +---+
+---+ +---+ +---+ +---+
| W |(A) o | W |(D) | W |(A) o | W |(B)
+---+ +---+ +---+ +---+
+---+ +---+ +---+ +---+
| W |(B) | W |(C) | W |(D) | W |(C)
+---+ +---+ +---+ +---+ +---+ +---+
| M | | M |
+---+ +---+In CASE IIa, Mrs. Astor is the hostess who was the only person to sit between a married couple. But either Mr. Astor or Mr. Davis has to be one of the men sitting opposite each other, so that more than one person sat between a married couple. This situation contradicts (3) and so CASE IIa is eliminated and CASE IIb is the correct case.
Then Mrs. Blake or Mrs. Davis must be the hostess, from (3). If Mrs. Blake is the hostess, then Mr. Crane sat next to her. Then Mr. Astor has to be one of the men sitting opposite each other, so that more than one person sat between a married couple. This situation contradicts (3) and so Mrs. Davis is the hostess.
Then, from (3), Mr. Astor sat next to Mrs. Davis while Mr. Davis sat next to Mrs. Blake, So Mr. Crane sat opposite Mr. Astor. And, from (4), Mr. Crane insulted the hostess.
(CASE IIb)
+---+
| M |(C)
+---+
+---+ +---+
| M |(B) | M |(D)
+---+ +---+
+---+ +---+
| W |(A) o | W |(B)
+---+ +---+
+---+ +---+
| W |(D) | W |(C)
+---+ +---+
+---+
| M |(A)
+---+
|
