4

Part of 2013 Serbia National Math Olympiad

Problems(1)

Partition of set {1,2,3,...,3n} into n subsets {a,b,c}

Source: Serbian National Olympiad 2013, Problem 4

Determine all natural numbers

b-a

for which there is a partition of

\{1,2,...,3n\}

n

pairwise disjoint subsets of the form

\{a,b,c\}

, such that numbers

b-a

c-b

are different numbers from the set

\{n-1, n, n+1\}

inductionpigeonhole principlecombinatorics proposedcombinatorics