5

Part of 1986 China National Olympiad

Problems(1)

China Mathematical Olympiad 1986 problem5

Source: China Mathematical Olympiad 1986 problem5

Given a sequence

1,1,2,2,3,3,\ldots,1986,1986

, determine, with proof, if we can rearrange the sequence so that for any integer

1\le k \le 1986

there are exactly

k

numbers between the two “

k

combinatorics unsolvedcombinatorics