document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=619582>Question 619582</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The Host gave each contestant a positive whole number and told them that the product of their whole numbers was either 15,20,24,or 28. The first contestant to determine the others number would be the winner. what was the losers number? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #389985 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=389985\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'll assume two contestants, A and B.\r<BR>\n" );
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document.write( "First off, if contestant A gets 15, 20, 24, or 28, he automatically wins and B's number is 1.\r<BR>\n" );
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document.write( "If A gets 6, 7, 8, 10, 12, or 14 (all of these numbers are factors of exactly one of the four given #s), A wins, and B's number will be either 2, 3, or 4.\r<BR>\n" );
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document.write( "If A gets any other factor of the given four #'s, he cannot immediately determine B's number.\r<BR>\n" );
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document.write( "Hence, if A gets 2, B can have either a 10, 12, or 14. B wins.\r<BR>\n" );
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document.write( "If A gets 3, B can have either 5 or 8. If B does not automatically respond with A's number, B cannot have 8, and therefore contestant A can conclude that B has 5.\r<BR>\n" );
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document.write( "If A gets 4, B can have either 5, 6, or 7. If B does not automatically respond with A's number, he cannot have 6 or 7. Therefore A can conclude that B has 5.\r<BR>\n" );
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document.write( "If A gets 5, B can have either 3 or 4. A cannot determine what number B has, so B wins by the above logic.\r<BR>\n" );
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document.write( "Therefore the possible losing numbers are 1, 2, and 5. Other than 1,2,3,4,5, no other numbers divide two or more of {15, 20, 24, 28}.\r<BR>\n" );
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