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 Calm down, people! (Posted on 2005-10-25)
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) +---+```

 Subject Author Date Puzzle Thoughts K Sengupta 2023-03-13 00:27:03 re: Reply. pcbouhid 2005-11-28 16:17:33 Reply. AJ Valadez 2005-11-28 14:05:39 re: Could this work? pcbouhid 2005-11-28 07:49:46 Could this work? AJ Valadez 2005-11-27 23:08:54 re: The solution is... Michael Miller 2005-10-31 21:00:51 The solution is... Salva 2005-10-31 20:02:48 re: Agree with Jacki ben Koostra 2005-10-31 16:40:53 re: answer...i think... Mindy Rodriguez 2005-10-30 21:51:40 answer...i think... Stephen Ticsay 2005-10-30 19:25:00 re(3): No Solution Yet? pcbouhid 2005-10-29 23:12:12 re(2): Solution - by hand Mindy Rodriguez 2005-10-29 21:39:50 re: Solution - by hand denise 2005-10-29 20:57:20 solved it!!.. i think denise 2005-10-29 20:53:06 re(2): No Solution Yet? Mindy Rodriguez 2005-10-29 18:59:38 re: Agree with Jacki Mindy Rodriguez 2005-10-29 17:46:12 re: No Solution Yet? Charlie 2005-10-29 17:35:45 No Solution Yet? Mindy Rodriguez 2005-10-29 17:31:50 re: Re: Charlies computer solution Charlie 2005-10-29 17:28:54 re: Re: Charlies computer solution Mindy Rodriguez 2005-10-29 17:25:53 re: The Solution by dopey915 is good Mindy Rodriguez 2005-10-29 17:19:22 retraction Mindy Rodriguez 2005-10-29 17:04:52 re: First Guess Mindy Rodriguez 2005-10-29 16:51:17 Re: Charlies computer solution Mindy Rodriguez 2005-10-29 16:48:22 Solution Mindy Rodriguez 2005-10-29 16:43:32 re: Hehe answer? pcbouhid 2005-10-28 11:32:10 Hehe answer? Quincy 2005-10-28 10:37:46 Guess 1 Donna Wade 2005-10-27 15:08:47 First Guess Mike 2005-10-27 13:30:28 re: Hand Solution pcbouhid 2005-10-26 22:06:01 Hand Solution Gamer 2005-10-26 19:44:18 re(3): Solution - by hand pcbouhid 2005-10-26 15:48:50 re(2): Solution - by hand Jacki 2005-10-26 15:34:08 re: The Solution - finally pcbouhid 2005-10-26 14:02:16 The Solution dopey915 2005-10-26 12:26:47 I didnīt see yet pcbouhid 2005-10-26 11:07:43 solution by hand Sean 2005-10-26 10:43:42 Agree with Jacki goFish 2005-10-26 10:23:38 re: Solution - by hand pcbouhid 2005-10-26 07:13:59 Solution - by hand Jacki 2005-10-25 18:17:25 re: Yes Jacki 2005-10-25 18:11:02 Yes Alissa 2005-10-25 17:54:56 computer solution (spoiler) Charlie 2005-10-25 11:16:24 re: Whose party is it anyway? pcbouhid 2005-10-25 10:16:22 Whose party is it anyway? goFish 2005-10-25 09:48:35

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