document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1058085>Question 1058085</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 120 students take an exam which is marked out of a 100 (with no fractional marks). No 3 students are awarded the same mark. What is the smallest possible number of pairs of students what are awarded the same mark? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #673261 by </B><A HREF=/tutors/aboutme.mpl?userid=LinnW><B>LinnW(1048)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=LinnW><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=LinnW><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=673261\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Each of 101 students receive a score of 0,1,2 ... 100<BR>\n" );
document.write( "Each of the remaining 19 students receives a score that is the same score<BR>\n" );
document.write( "as one other students.<BR>\n" );
document.write( "For example, we could have scores in descending order of<BR>\n" );
document.write( "100,100,99,99,98,98,97,97,96,96,95,95,94,94,93,93,92,92,91,91,<BR>\n" );
document.write( "90,90,89,89,88,88,87,87,86,86,85,85,84,84,83,83,82,82<BR>\n" );
document.write( "81,80,... 0<BR>\n" );
document.write( "Notice that if we do not have 19 students with the same score<BR>\n" );
document.write( "we will have less than a total of 120 students. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );