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Chair Cue (Posted on 2014-03-07) Difficulty: 3 of 5
       A
   +---+---+
   |   |   |
 J +---+---+ B
   |   |   | 
   |   |   |
   |   |   |
 I +---+---+ C
   |   |   |   D         
   |   |   +---+----+
   |   |       |    |
 H +---+-------+----+ E
   |   |       |    |
   +---+-------+----+
       G       F
Mr. and Mrs. Larchmont invited four married couples to a dinner party. For the party, chairs A to J were placed around an L-shaped table as shown above.
  1. Every woman sat next to her husband.
  2. A is next to B, B is next to C, C is next to D, D is next to E, E is next to F, F is next to G, G is next to I and, I is next to J.
  3. Every woman sat directly across from a man. (Chairs at the ends of a dashed line denotes "directly across" from each other.
  4. Mrs. Larchmont sat to the right of Mr. larchmont.
  5. Mrs. Larchmont was the only woman who did not sit next to a woman.
In which of the chairs from A to J inclusively did Mrs. Larchmont sit?

Notes:
(i) A person sitting next to another person implies that the other person is sitting next to the said person. For example, A is next to B implies that B is next to A and vice versa.

(ii) "To the right of" is defined as the one they see when they turn their head to their own right. For example, F to the right of G.

No Solution Yet Submitted by K Sengupta    
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Solution Analytical Solution (spoiler) Comment 2 of 2 |
Assume A&B are a couple.  Then the other couples are C&D, E&F, G&H, I&J.
Let A be gender 1, and B gender 2.
Then J, who sits across from B, is a 1 and spouse I is a 2.
Then C, who sits across from I, is a 1 and spouse D is a 2.
Then F, who sits across from D, is a 1 and spouse E is a 2.
Then H, who sits across from E, is a 1 and spouse G is a 2.
But there are two 1's (C&H) who are surrounded by 2's.
And there are two 2's (B&I) who are surrounded by 1's.
So Mrs. Larchmont cannot be gender 1 or 2.
Therefore, our initial assumption is wrong, and A&B are not a couple.

Therefore, A&J are a couple.  The other couples are B&C, D&E, F&G, H&I.
Let A be gender 1, and J gender 2.
Then B, who sits across from J, is a 1 and spouse C is a 2.
Then I, who sits across from C, is a 1 and spouse H is a 2.
Then E, who sits across from H, is a 1 and spouse D is a 2.
Then F, who sits across from D, is a 1 and spouse G is a 2.
Now J is the only 1 surrounded by 2's.
And I is the only 2 surrounded by 1's.
So Mrs. Larchmont must be I or J.
But I sits to the left of his spouse, so Mrs. Larchmont is J.

  Posted by Steve Herman on 2014-03-07 13:54:53
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