Amelia, Beulah, Carrie, Dennis and Elwood attended a supper party with their spouses at Loverly's Restaurant. Chairs for the five couples were arranged around an L-shaped table as shown in the diagram below.

    
         a   
     +---------+        
     |         | 
     |         |   
    j|         |b    
     |         |      
     |         |    
     |         |
    i|         |c   
     |         |   
     |         |  d
     |         +---------+       
    h|                   |
     |                   |e
     |                   | 
     +-------------------+
        g        f 

At the table:

1. Amelia's husband sat next to Dennis' wife.
2. Beulah's husband was the only man who sat alone at one side of the table.
3. Carrie's husband was the only man who sat between two women.
4. No woman sat between two women.
5. Each man sat opposite his wife.
6. Elwood's wife sat on the Professor's right.

Who was the Professor?

Notes:

(i) "Between two women" means to the left of one woman and to the right of another woman, around the perimeter of the table.

(ii) Similarly "sat next to" means either immediately to the right or, immediately to the left of a given seat around the perimeter of the table. For example, chair-e and chair-f are next to each other.

From clue 2, one of a, d, e are Male (M) and the other 
two are female.

Assume seat a is male.  Then from clue 5 (each man sat
opposite his wife), the table must be arranged
   abcdefghij
   M??FFMFM??
Seat c must be M from clue 4, which makes i F, but this
violates clue 3, because now both h and f are men 
sitting between women.  Therefore, a is Female.

Assume seat e is male.  Then from clue 5 (each man sat 
opposite his wife), the table must be arranged
   abcdefghij
   F??FMMMF??
But now there is no way to seat the last two couples 
without either having 3 F's in a row or two M each 
surrounded by women.  Therefore, seat e is Female.

Which makes seat d Male.  The table must be arranged
   abcdefghij
   F??MFFMM??
   
If seat j is F, then i must be M to avoid three F's in
a row.  That makes b and c, respectively, M and F, 
which violates clue 3, because both b and d are two M 
each surrounded by women.  Therefore, seat j is Male, 
and the full arrangement is
   abcdefghij
   FFMMFFMMFM
   
 Now that the table is set, lets put out name plates.
 From clue 2, d is Beulah's husband and f is Beulah.
 From clue 3, j is Carrie's husband and b is Carrie.
 From clue 1, Amelia's husband cannot be c or g, 
   so he is h and e is Amelia.
 From clue 1, Dennis' wife is i so Dennis is c.
 
 Full solution:
 
 a Elwood's wife
 b Carrie (Professor)
 c Dennis
 d Beulah's husband
 e Amelia
 f Beulah
 g Elwood
 h Amelia's husband
 i Dennis' wife
 j Carrie's husband

Posted by Steve Herman on 2013-04-26 20:07:52