document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1208363>Question 1208363</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Prove that given any set of $17$ integers, there exist nine of them whose sum is divisible by $2.$ </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #846741 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52933)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=846741\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Prove that given any set of $17$ integers, there exist nine of them whose sum is divisible by $2.$<BR>\n" );
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document.write( "As it is worded, &nbsp;printed, &nbsp;posted and presented, &nbsp;it is &nbsp;TOTALLY &nbsp;and &nbsp;FATALLY &nbsp;wrong statement.\r<BR>\n" );
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document.write( "Take, &nbsp;for example, &nbsp;17 integers, &nbsp;all equal to &nbsp;1, &nbsp;and you will &nbsp;NEVER get &nbsp;9 &nbsp;addends,<BR>\n" );
document.write( "giving an even sum. &nbsp;&nbsp;Their sum always will be &nbsp;9.\r<BR>\n" );
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document.write( "Or, &nbsp;if this example does not convince you, &nbsp;take first 17 odd integer numbers\r<BR>\n" );
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document.write( "    1, 3, 5, 7, . . . 31, 33.\r<BR>\n" );
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document.write( "Using these numbers, &nbsp;you will never get &nbsp;9 &nbsp;of them with an even sum.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Where did you get this gibberish ? &nbsp;&nbsp;&nbsp;What is the source ?\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Just a shamefully low level of Math composing.\r<BR>\n" );
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document.write( "I placed this formulation in my Google browser and requested for search.\r<BR>\n" );
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document.write( "It generates first output created by Artificial Intelligence (AI).  \r<BR>\n" );
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document.write( "It becomes making some reasoning, but from its output,<BR>\n" );
document.write( "it is clear that this AI incorrectly understands the problem.\r<BR>\n" );
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document.write( "The link is \r<BR>\n" );
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document.write( "https://www.google.com/search?q=Prove+that+given+any+set+of+%2417%24+integers%2C+there+exist+nine+of+them+whose+sum+is+divisible+by+%242.%24&rlz=1C1CHBF_enUS1071US1071&oq=Prove+that+given+any+set+of+%2417%24+integers%2C+there+exist+nine+of+them+whose+sum+is+divisible+by+%242.%24&gs_lcrp=EgZjaHJvbWUyBggAEEUYOdIBCTE4MTFqMGoxNagCCLACAQ&sourceid=chrome&ie=UTF-8\r<BR>\n" );
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document.write( "On the way, this AI generates a blatant nonsense.\r<BR>\n" );
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document.write( "At the very end, it confesses that\r<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "    Generative AI is experimental. Answers might be inaccurate or misleading. \r\n" );
document.write( "    Double-check for accuracy.\r\n" );
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document.write( "It is precisely the case when this AI works INCORRECTLY.\r<BR>\n" );
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document.write( "Still is not trained to solve such problems.\r<BR>\n" );
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document.write( "Had it worked in a right way, it should/(it must) recognize that the problem is posed INCORRECTLY.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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