Who is a Liar, Who Tells the Truth?Date: 9/4/96 at 19:7:34 From: Anonymous Subject: Who is a Liar, who Tells the Truth The inhabitants of a certain island have a strange characteristic: those who are swimmers always tell the truth, and those who are non- swimmers always lie. You visit the island and meet a group of three native inhabitants. You ask the first person, "Are you a swimmer?" The answer is unintelligible. The second person immediately says, "That was 'yes.' I am a swimmer, too." The third person says, "They are both lying." Is each of these three people a swimmer or a nonswimmer? My answer: The first is a nonswimmer, the second is also a nonswimmer, the third one is a swimmer. Date: 9/4/96 at 21:54:41 From: Doctor Robert Subject: Re: Who is a Liar, who Tells the Truth Put yourself in the place of the second of the three natives. If the first person is a swimmer he will say "I am a swimmer." If the first person is a non-swimmer, he will also say "I am a swimmer" (because he always lies). So, the thing that the second person hears is "I am a swimmer." When the second person says that the first person says he is a swimmer, the second person is telling the truth and is therefore a swimmer. Now, the third person says that the second person is lying - which is wrong. So that makes the third person a non-swimmer. Unfortunately, we do not know whether the first person is a swimmer or non-swimmer. Using S for swimmer and N for non-swimmer, the possibilities are SSN or NSN [See also the Classic Problem "Liars and Truthtellers" in the Dr. Math FAQ: http://mathforum.org/dr.math/faq/faq.liar.html .] -Doctor Robert, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
Search the Dr. Math Library: |
[Privacy Policy] [Terms of Use]
Ask Dr. Math^{TM}
© 1994- The Math Forum at NCTM. All rights reserved.
http://mathforum.org/dr.math/