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Calm down, people! (Posted on 2005-10-25) Difficulty: 2 of 5
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?

  Submitted by pcbouhid    
Rating: 3.3333 (9 votes)
Solution: (Hide)
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)             
                                           +---+

Comments: ( You must be logged in to post comments.)
  Subject Author Date
re: Reply.pcbouhid2005-11-28 16:17:33
Reply.AJ Valadez2005-11-28 14:05:39
re: Could this work?pcbouhid2005-11-28 07:49:46
Could this work?AJ Valadez2005-11-27 23:08:54
re: The solution is...Michael Miller2005-10-31 21:00:51
SolutionThe solution is...Salva2005-10-31 20:02:48
Solutionre: Agree with Jackiben Koostra2005-10-31 16:40:53
re: answer...i think...Mindy Rodriguez2005-10-30 21:51:40
Solutionanswer...i think...Stephen Ticsay2005-10-30 19:25:00
re(3): No Solution Yet?pcbouhid2005-10-29 23:12:12
re(2): Solution - by handMindy Rodriguez2005-10-29 21:39:50
re: Solution - by handdenise2005-10-29 20:57:20
solved it!!.. i thinkdenise2005-10-29 20:53:06
re(2): No Solution Yet?Mindy Rodriguez2005-10-29 18:59:38
re: Agree with JackiMindy Rodriguez2005-10-29 17:46:12
re: No Solution Yet?Charlie2005-10-29 17:35:45
No Solution Yet?Mindy Rodriguez2005-10-29 17:31:50
Solutionre: Re: Charlies computer solutionCharlie2005-10-29 17:28:54
re: Re: Charlies computer solutionMindy Rodriguez2005-10-29 17:25:53
re: The Solution by dopey915 is goodMindy Rodriguez2005-10-29 17:19:22
retractionMindy Rodriguez2005-10-29 17:04:52
re: First GuessMindy Rodriguez2005-10-29 16:51:17
Re: Charlies computer solutionMindy Rodriguez2005-10-29 16:48:22
SolutionSolutionMindy Rodriguez2005-10-29 16:43:32
re: Hehe answer?pcbouhid2005-10-28 11:32:10
Hehe answer?Quincy2005-10-28 10:37:46
Guess 1Donna Wade2005-10-27 15:08:47
First GuessMike2005-10-27 13:30:28
re: Hand Solutionpcbouhid2005-10-26 22:06:01
Hand SolutionGamer2005-10-26 19:44:18
re(3): Solution - by handpcbouhid2005-10-26 15:48:50
re(2): Solution - by handJacki2005-10-26 15:34:08
re: The Solution - finallypcbouhid2005-10-26 14:02:16
SolutionThe Solutiondopey9152005-10-26 12:26:47
I didnīt see yetpcbouhid2005-10-26 11:07:43
solution by handSean2005-10-26 10:43:42
Agree with JackigoFish2005-10-26 10:23:38
re: Solution - by handpcbouhid2005-10-26 07:13:59
SolutionSolution - by handJacki2005-10-25 18:17:25
re: YesJacki2005-10-25 18:11:02
YesAlissa2005-10-25 17:54:56
Solutioncomputer solution (spoiler)Charlie2005-10-25 11:16:24
re: Whose party is it anyway?pcbouhid2005-10-25 10:16:22
Whose party is it anyway?goFish2005-10-25 09:48:35
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