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This puzzle appeared in an article by Martin Gardner. It goes like this:

Miss green, Miss Black and Miss Blue are out for a stroll together. One is wearing a green dress, one a black dress and the other a blue dress. "Isn't it odd" says Miss Blue, "that our dresses match our last names, but not one of us is wearing a dress that matches her own name".

The question is $$What\ color\ is\ each\ lady's\ dress$$ $$ $$

The solution offered in various places on the net is: $$ $$

$$ \begin{array}{c|lcr} \text{L/C} & \text{Black} & \text{Blue} & \text{Green} \\ \hline \text{Ms. Black} & \text{.} & \text{Y} & \text{.} \\ \text{Ms. Blue} & \text{.} & \text{.} & \text{Y} \\ \text{Ms. Green} & \text{Y} & \text{.} & \text{.} \end{array} $$ $$ $$

This gives the impression that this brain teaser has a unique solution but, I don't believe that is the case. If one reflects the above solution along the diagonal, that produces a second solution which must be correct if the first one was correct.$$ $$

$$ \begin{array}{c|lcr} \text{L/C} & \text{Black} & \text{Blue} & \text{Green} \\ \hline \text{Ms. Black} & \text{.} & \text{.} & \text{Y} \\ \text{Ms. Blue} & \text{Y} & \text{.} & \text{.} \\ \text{Ms. Green} & \text{.} & \text{Y} & \text{.} \end{array} $$

$$ $$ It seems obvious (to me) that this problem has 2 solutions, not just one, as this brainteaser implies by simply asking "What color is each lady's dress". That said, I thought I'd ask this question in case there is something I have missed.

Specifically, does this problem have a unique solution or not ?

Edit

The original puzzle adds $$"so\ what" said\ the\ lady\ in\ black$$ which causes the puzzle to have a unique solution.

See the answer by lulu below which explains why that statement makes a difference. I originally omitted that part of the puzzle because I mistakenly read: "so what" said Miss Black, which makes no difference unlike when the question is asked by the lady in black (not Miss Black).

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    $\begingroup$ You changed the puzzle. The original ends with the line "So what?" says the lady in black. So we know Miss Blue isn't wearing black. $\endgroup$
    – lulu
    Commented Mar 11, 2017 at 18:49
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    $\begingroup$ @lulu And there we have it! $\endgroup$ Commented Mar 11, 2017 at 18:50
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    $\begingroup$ @Peter: because the lady in black replied to Miss Blue, so she cannot be Miss Blue. $\endgroup$ Commented Mar 11, 2017 at 19:02
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    $\begingroup$ amWhy: Now I got it :-). It is the lady wearing black who asks "so what?" not Miss Black (as I was stuck on.) Thank you, yes, that does make a big difference in the solution. @lulu: thank you for the clear explanation. "Had the line been spoken by Miss Black we would have learned nothing", that was the source of my misunderstanding. I was stuck on the comment being made by Miss Black instead of "the lady in black". $\endgroup$
    – MathAddict
    Commented Mar 11, 2017 at 19:34
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    $\begingroup$ Glad to help, MathAddict!! $\endgroup$
    – amWhy
    Commented Mar 11, 2017 at 19:36

3 Answers 3

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As requested in the comments:

Gardner's version of the puzzle ends with a line which is omitted here: $$\text {"So what?", said the lady in black.}$$

Note: a reference can be found here.

Somewhat surprisingly, that changes everything. It adds the information that Miss Blue is not wearing black (as she wouldn't have replied to herself, nor would she have disparaged her own observation). That makes the solution unique.

Note how delicate this information is. Had the line been spoken by Miss Black, we'd have learned nothing. Had it been spoken by "the lady in blue" we'd have learned nothing (as we already knew that Miss Blue was not wearing blue).

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    $\begingroup$ Doesn't this mean that the solution "offered in various places on the net" is the wrong one, though? $\endgroup$
    – jwodder
    Commented Mar 11, 2017 at 23:42
  • $\begingroup$ @jwodder: my mistake, after reading your comment I noticed that I put the solutions backwards. I'm going to edit the question to reflect the solution found on the net. $\endgroup$
    – MathAddict
    Commented Mar 12, 2017 at 0:02
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There are two options not matching. If they sit in a triangle wearing their own colours, they can rotate the dresses once and then again, both of these cases nobody wears their own.

'"So what?" said the lady in black.' Indicates that the lady in black is not Miss Blue, leaving only one possibility.

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    $\begingroup$ It's worth pointing out that you changed the question after I answered. $\endgroup$ Commented Mar 13, 2017 at 18:18
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Since Ms. Black is not wearing the black dress, she must be wearing either the green dress or the blue dress.

Suppose she is wearing the green dress. That leaves the blue and black dresses for Ms. Blue and Ms. Green. Ms. Blue is not wearing the blue dress so she must be wearing the black dress and Ms. Green the blue dress.

Yes, one solution is "Ms. Black is wearing the green dress, Ms. Blue is wearing the black dress, and Ms. Green is wearing the blue dress.

Suppose Ms. Black is wearing the blue dress. That leaves the green and black dresses for Ms. Blue and Ms. Green. Ms. Green is not wearing the green dress so she must be wearing the black dress and Ms. Blue the green dress.

Yes, another solution is "Ms. Black is wearing the green dress, Ms. Blue is wearing the green dress, and Ms. Green is wearing the black dress.

There are two distinct solutions.

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