document.write( "Question 1058085: 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? \n" ); document.write( "
Algebra.Com's Answer #673261 by LinnW(1048)\"\" \"About 
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Each of 101 students receive a score of 0,1,2 ... 100
\n" ); document.write( "Each of the remaining 19 students receives a score that is the same score
\n" ); document.write( "as one other students.
\n" ); document.write( "For example, we could have scores in descending order of
\n" ); document.write( "100,100,99,99,98,98,97,97,96,96,95,95,94,94,93,93,92,92,91,91,
\n" ); document.write( "90,90,89,89,88,88,87,87,86,86,85,85,84,84,83,83,82,82
\n" ); document.write( "81,80,... 0
\n" ); document.write( "Notice that if we do not have 19 students with the same score
\n" ); document.write( "we will have less than a total of 120 students.
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