The Five Slaves

Logic Level 1

A Caliph proposed a problem to Beremiz Samir.

The problem is:

He bought five women slaves, and two of these slaves have black eyes and the other three have blue eyes.

The blue eyes women always lies, and the black eyes women always tell the truth.

In a few moments the five of them will be brought here, all of their faces covered by a heavy veil, which will make it impossible for Beremiz see their faces.

Beremiz can only ask three questions for any slave (not three questions for each, but only three question in total). The objective is to know the color of eyes of each one.

The slaves was standing in line, and Beremiz asked to the first one:

"What color is your eyes?"

And she replied in chinese, and he don't understood.

Then, he ask for the second slave:

"What was the reply that the first woman just gave?"

The second replied:

"She said, 'My eyes are blue'."

Finally Beremiz ask to the tird slave:

"What color are the eyes of those two girls I have just questioned?"

And the third replied:

"The first girl has black eyes and the second blue eyes".

After it Beremiz gave the correct answer for the Caliph.

The question is:

What is the color of eyes of the last two slaves that was not interviewed?

Problem from the book: "The Man Who Counted (O Homem Que Calculava) - Malba Tahan"
Blue Black

Victor Paes Plinio by Victor Paes Plinio , 21, Brazil

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5 solutions

The solution that is in the book is:

The first one only can answer "My eyes are black" because, if she have black eyes she will tell the truth. But if she have blue eyes she will lie saying that her eyes are black. Thus Beremiz without need to understand chinese he already knew the answer.

The second said: "She said, 'My eyes are blue'."

Knowing the fact that the first one only can reply "My eyes are black", now Beremiz know the color of she's eyes, that is blue because she lied.

The third replied:

"The first girl has black eyes and the second blue eyes"

She told the truth, the first have black eyes, and the second have blue eyes. Thus she have black eyes.

They were 2 girls with black eyes (the first and the third) and 3 with blue eyes (the second and the other two girls).

Thus the answer is "Blue".

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Nehemiah Osei
Aug 23, 2015

When the first slave spoke, it says no one understood but the second slave was able to translate her. Meaning she was lying since in actual fact no one understood. The nature of the question implies that the last two have the same eye colour.

We know that the second slave has blue eyes and third slave was able to tell. This means she has black eyes.

Obviously, the last two do not have black eyes since there are only two slaves with black eyes.

Therefore, the last two slaves have blue eyes.

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Logically, the options imply that the remaining two has the same color.
Answer of the third implies that first and third have different colors.
So the first three are not Blue. So first three must have two black.
So the remaining must be two BLUE.
O R OR If the first was Blue, (LIAR), she would say "BLACK". If she was Black., then also she would say "BLACK".
So the second is lying. She IS BLUE. So the first IS "BLACK".
Third is therefore true. Third IS "BLACK".
So remaining two are "BLUE".



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Cynthia Chan
Aug 23, 2015

The first woman answered in Chinese, so it's most likely that she IS Chinese, and therefore, has black eyes. The second woman, therefore, lied, and thus has blue eyes, which makes what the third woman say the truth, and making her have black eyes.

Thus the other two women have blue eyes.

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" most likely that she IS Chinese". However your solution is based on this only. So your solution is most likely, but not definite !!

Niranjan Khanderia - 5 years, 9 months ago 
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Slaves : (1) (2) (3) (4) (5)

1. When slave (1) spoke, we cannot tell immediately if she is a liar or not.
2. Assuming (2) is honest, then (1) has blue eyes (LIAR)
3. But the statement of (3) contradicts (2), so (3) has blue eyes (LIAR)
4. From 3, we can tell (2) has black eyes

So we have 2 LIARS and 1 HONEST slaves right now. But there are only 3 LIARS, so we have 1 LIAR and 1 HONEST slaves (the last 2 slaves not called). This is absurd since both slaves must have the same eye color.

If we change our assumption that (2) is honest, that is, we assume right now (2) is a LIAR, we arrive at the conclusion that the last two slaves both have blue eyes.

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