Who's Right?

Logic Level 2

Charles and his friends, Winston and Joseph, took a test. Upon reviewing the first question, they say as follows:

  • Charles: "I'm right."
  • Joseph: "Two of us are right."
  • Winston: "None of us are right."

Their teacher comes up to them with the answer sheet and says that two of their statements are correct. Of Charles, Winston, and Joseph, whose answers (not their statements) must be correct no matter what?

Joseph and Charles Joseph Neither Charles

Ian Watson-Hemphill by Ian Watson-Hemphill , 20, USA

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3 solutions

If Winston's statement was correct, then (as it is mutually exclusive with Charles and Joseph's statements) there would only be one correct statement, so Winston's statement must be incorrect. The only way for both Charles to be right and for there to be at least two people right is if

  • Charles's answer is right, Joseph's answer is right, Winston's answer is wrong
  • Charles's answer is right, Joseph's answer is wrong, Winston's answer is right

Joseph's answer might be wrong, and Winston's answer might be wrong, but Charles's answer is correct in both cases, so Charles's answer must be right.

3 Helpful 0 Interesting 1 Brilliant 0 Confused
X X
Apr 25, 2018

If Winston's statement is correct,the other two statements will be false,and there will be only a correct statement.So Winston's statement is incorrect,then Charles's statement(and Joseph's) is true,that means Charles got it right.According to Joseph's statement,the other one who got it right may be Joseph or Winston.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Then shouldn't the answer be 'Joseph and Charles'?

Siva Budaraju - 3 years, 1 month ago

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Thank you.I editted my solution a little.

X X - 3 years, 1 month ago
Stephen Mellor
May 9, 2018

Let's say Winston's statement is true. This means that Charles and Joseph's statements can't be true, so their aren't two correct. Therefore, Charles and Joseph are telling it true. Therefore Charles is obviously correct as he says it. However, the second correct person (as Joseph said there are 2) could either be Joseph or Winston so only Charles \boxed{\text{Charles}} is definitely correct.

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