Mr. and Mrs. Astor, Mr. and Mrs. Blake, Mr. and Mrs. Crane, and Mr. and Mrs. Davis were seated around a table as shown:

                      +---+
                      | 1 |
                +---+ +---+ +---+
                | 8 |       | 2 |
                +---+       +---+
            +---+               +---+
            | 7 |       o       | 3 |
            +---+               +---+
                +---+       +---+
                | 6 |       | 4 |
                +---+ +---+ +---+   
                      | 5 |
                      +---+

1) Mrs. Astor was insulted by Mr. Blake who sat next to her on her left.

2) Mr. Blake was insulted by Mrs. Crane who sat opposite him across the center of the table.

3) Mrs. Crane was insulted by the hostess who was the only person who sat between a married couple.

4) The hostess was insulted by the only person who sat between two men.

Who insulted the hostess?

The insultor is Mr. Crane.

 

Using the diagram, start with Mrs. A in 1, Mr. B in 2, and Mrs. C in 6.  The insulter (I) cannot sit next to a woman, so I cannot be 2, 5, 7, or 8.  Mrs. C was insulted by the hostess (H) so Mrs. C is not H (she didn’t insult herself).  Mr. A cannot be in 3 (Mr. B cannot be the hostess, which we presume is female). 

<o:p> </o:p>

Examining the possible placements of males and females, the only possible combination that results in only one instance of a person between two males is 1 = F, 2 = B, 3 = B, 4 = B, 5 = F, 6 = F, 7 = M, 8 = F.  So the person in position 3, a male, must be the Insultor.  But who is it?  We already know that it is not Mr. B or Mr. A.  

<o:p> </o:p>

Suppose 3 is Mr. D.  Now suppose Mr. A is in 7.  This leaves Mr. C in 4.  But that combination results in two instances of a person sitting between a married couple.  Specifically, position 8 is between the two Astors, and position 5 is between the two Cranes.  So Mr. A cannot be in 7. 

<o:p> </o:p>

So still with Mr. D in 3, try Mr. A in position 4, and Mr. C in 7.  If Mrs. B is in position 8, and Mrs. D is in 5, then we again have two instances of a person sitting between a married couple.  Specifically, position 1 is between two Blakes, and position 4 is between two <st1:City w:st="on"><st1:place w:st="on">Davises</st1:place></st1:City>.  So instead, try Mrs. D in 8, and Mrs. D in 5.  This results in a situation where no one is sitting between a married couple.  So Mr. A cannot be in 4, and therefore Mr. D cannot be in 3.

<o:p> </o:p>

This leaves Mr. C sitting in 3 as the Insultor.  And by similar logic with placing the remaining males and females, the only combination that fits the criteria is:  1 = Mrs. A, 2 = Mr. B, 3 = Mr. C (I), 4 = Mr. D, 5 = Mrs. B, 6 = Mrs. C, 7 = Mr. A, and 8 = Mrs. D (H)

 

Posted by dopey915 on 2005-10-26 12:26:47