document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1146387>Question 1146387</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Numbers are drawn from 100 integers 1 to 100. At least how many numbers is/are drawn at random to ensure that there are two numbers whose sum is 30? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #767654 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=767654\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "For the sum of two different positive integers to be 30, the largest possible value for the smaller of the two is 14.<br><BR>\n" );
document.write( "So the worst case is to draw all the numbers from 15 to 100 before drawing any number less than 15.<br><BR>\n" );
document.write( "That's 86 numbers, from 15 to 100 inclusive, without having a sum of 30 with two of them.<br><BR>\n" );
document.write( "Then the 87th number will be less than 15; it will match up with a number already drawn to make a sum of 30.<br><BR>\n" );
document.write( "ANSWER: 87 numbers need to be drawn to assure that two of them have a sum of 30. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );