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match-score question

Submitted by qgsravya on Mon, 2007-10-29 23:31

 

In a certain cross-university meet between two colleges of 10 runners each, a runner who finishes in the Nth position contributes N to his college score.  The college with the lower score wins.  If there are no ties among the runners, how many different winning scores are possible?

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Posted on: Mon, 2007-10-29 23:33 #1
answer
Total score 20 + 19 + . . . = 20 x 21/ 2 = 210
 
Max Score with which one college can win the competition is 104
Minimum score to win = 1 + 2 + . . . . + 10 = 55
 

Possible Different scores = 104 – 54 = 50

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