document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1180837>Question 1180837</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Of the 30 students in my class, 11 practice taekwondo, 11 play piano, and 20 take lessons at AoPS. 4 students play piano and go to AoPS, 3 students do taekwondo and play piano, 5 student go to AoPS and practice taekwondo, and 3 students do none of these. How many students do all 3? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #810630 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52879)</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=810630\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Of the 30 students in my class, 11 practice taekwondo, 11 play piano, and 20 take lessons at AoPS. <BR>\n" );
document.write( "4 students play piano and go to AoPS, 3 students do taekwondo and play piano, 5 student go to AoPS and practice taekwondo, <BR>\n" );
document.write( "and 3 students do none of these. How many students do all 3?<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( "    In this problem, you are given the number of elements of the entire \"universal\" set (class);\r\n" );
document.write( "    the number of elements in its three subsets (11, 11 and 20);\r\n" );
document.write( "    the number of elements in in-pairs intersections of these three subsets (4, 3 and 5),\r\n" );
document.write( "    the number of elements in the UNION of the three subsets (27 = 30-3).\r\n" );
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document.write( "They want you find the number of elements  \" x \"  in the triple intersection of subsets.\r\n" );
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document.write( "Apply the inclusion-exclusion principle\r\n" );
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document.write( "    27 = 11 + 11 + 20 - 4 - 3 - 5 + x    (alternate sum)\r\n" );
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document.write( "or\r\n" );
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document.write( "    27 = 30 + x\r\n" );
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document.write( "This equation has no solution in integer non-negative numbers.\r\n" );
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document.write( "        THEREFORE, the posed problem HAS NO SOLUTIONS.\r\n" );
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document.write( "        It describes a situation, which NEVER MAY HAPPEN.\r\n" );
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document.write( "On Inclusion-Exclusion principle, read this Wikipedia article\r<BR>\n" );
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document.write( "https://en.wikipedia.org/wiki/Inclusion%E2%80%93exclusion_principle\r<BR>\n" );
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document.write( "Had your problem be posed correctly, &nbsp;I would be happy to solve it and to teach you.\r<BR>\n" );
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document.write( "Moreover, &nbsp;had it be posed correctly, &nbsp;I would add the list of relevant lessons \r<BR>\n" );
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document.write( "and similar solved problems from the archive of this forum as a bonus for you.\r<BR>\n" );
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document.write( "But at the given badly circumstances, &nbsp;I will not do it . . . \r<BR>\n" );
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document.write( " </SPAN>\n" );
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