perplexus.info :: Logic : Chair Cue

Chair Cue (Posted on 2014-03-07)

       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.

Every woman sat next to her husband.
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.
Every woman sat directly across from a man. (Chairs at the ends of a dashed line denotes "directly across" from each other.
Mrs. Larchmont sat to the right of Mr. larchmont.
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.

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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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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