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4

Part of 2012 Vietnam National Olympiad

Problems(1)

n boys and n girls in a row, students get candies

Source: Vietnamese National Mathematical Olympiad 2012-P4

2/8/2012
Let nn be a natural number. There are nn boys and nn girls standing in a line, in any arbitrary order. A student XX will be eligible for receiving mm candies, if we can choose two students of opposite sex with XX standing on either side of XX in mm ways. Show that the total number of candies does not exceed 13n(n2−1).\frac 13n(n^2-1).
combinatorics unsolvedcombinatorics