document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1181761>Question 1181761</A>: <I><SPAN STYLE=\"word-break: break-all;\"> James, Alex, and Linda were playing inside of their classroom. One of them broke the window. When their teacher asked who broke the window, she got these replies:\r<BR>\n" );
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document.write( "Linda: James broke the window!<BR>\n" );
document.write( "James: I didn't break it!<BR>\n" );
document.write( "Alex: Neither did I!\r<BR>\n" );
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document.write( "If two of the children lied, then who broke the window? </SPAN>\n" );
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document.write( "Answer:  Alex broke the window\r<BR>\n" );
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document.write( "Explanation:\r<BR>\n" );
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document.write( "Assume Linda is telling the truth. If so, then James is one of the two liars and he's the one that broke the window. At the same time, Alex is the other liar, which must mean he broke the window. We have a contradiction because only one kid broke the window. \r<BR>\n" );
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document.write( "This ultimately means Linda is not telling the truth, and we can conclude that James did not break the window. \r<BR>\n" );
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document.write( "So either Alex or Linda broke the window. \r<BR>\n" );
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document.write( "Now assume that Alex is telling the truth, which means we assume he didn't break the window. That makes James and Linda the two liars. <BR>\n" );
document.write( "If James is lying, then he broke the window. <BR>\n" );
document.write( "If Linda is lying, then the truth is actually \"James did not break the window\".\r<BR>\n" );
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document.write( "We have another contradiction. So we rule out the scenario that Alex is being honest.\r<BR>\n" );
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document.write( "The only thing left is to assume that James is the one telling the truth. He claims he didn't break the window, which matches with the conclusion made at the end of the first scenario (when we concluded that Linda wasn't telling the truth).\r<BR>\n" );
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document.write( "If Alex is lying, then he broke the window because it flips his original statement \"I didn't break the window\" (paraphrased) to \"I did break the window\". At the same time, Linda's original statement \"James broke the window\" is flipped to \"James did not break the window\". \r<BR>\n" );
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document.write( "In this third scenario, we can see that no contradictions happen. Since it's the last scenario left, and we've crossed out all the other previous ones, this must mean this scenario is the definitive case of what's going on. We've shown that James is the only kid telling the truth and the other students are lying. Furthermore, we've concluded that Alex is the one that broke the window. <BR>\n" );
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