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)![]() ![]() You can put this solution on YOUR website! 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. \n" ); document.write( " |