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A school has 200 students. These are special students, some of them ALWAYS tell the truth, and the rest of them NEVER tell the truth. Among the subject areas of math, science, and social studies, each student has one favorite. A survey was conducted, each student was asked three yes or no questions: “Do you like math the most?” “Do you like science the most?” “Do you like social studies the most?”

The results were as follows:

104 students said “yes,” they like math the most.

86 students said “yes,” they like science the most.

60 students said “yes,” they like social studies the most.

How many students tell the truth, and how many do not?

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A school has 200 students. These are special students, some of them ALWAYS tell the truth, and the rest of them NEVER tell the truth. Among the subject areas of math, science, and social studies, each student has one favorite. A survey was conducted, each student was asked three yes or no questions: “Do you like math the most?” “Do you like science the most?” “Do you like social studies the most?”

The results were as follows:

104 students said “yes,” they like math the most.

86 students said “yes,” they like science the most.

60 students said “yes,” they like social studies the most.

How many students tell the truth, and how many do not?

Hmmmm ... I could be wrong, but my gut tells me that you would have to know the distribution of the favorites among the students. If every student liked math, the results would be different than if every student liked science. Right?

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Hmmmm ... I could be wrong, but my gut tells me that you would have to know the distribution of the favorites among the students. If every student liked math, the results would be different than if every student liked science. Right?

In this problem you don't need to.

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In this problem you don't need to.

A truthteller will only answer "yes" once but a liar will say "yes" twice. 250 "yes"s are tallied so 50 of the 200 students are Liars.

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I think it's like this?

There are 250 responses but only 200 students. All the liars said YES twice. Therefore there are 50 liars and 150 who tell the truth.

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Nice. I like it when the problem has a clear, simple, yet non-intuitive answer. Of course, I like it better when I think of that answer myself. I'll take what I can get. :)

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Good work slinks. Good job redshift. :D

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